The algorithm follows a mathematical approach that i will explain later, and it does confirm Martin's referenced list, basing on this program:
stored=[2, 3, 3, 4, 6, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 10, 6, 10, 8, 8, 6, 10, 8, 8, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 14, 8, 8, 8, 14, 8, 14, 12, 12, 8, 8, 8, 14, 8, 14, 12, 12, 8, 14, 12, 12, 10, 10, 10, 10, 8, 8, 8, 14, 8, 14, 12, 12, 8, 14, 12, 12, 10, 10, 10, 10, 8, 14, 12, 12, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 18, 10, 10, 10, 10, 10, 10, 10, 18, 10, 10, 10, 18, 10, 18, 16, 16, 10, 10, 10, 10, 10, 10, 10, 18, 10, 10, 10, 18, 10, 18, 16, 16, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 10, 10, 10, 10, 10, 10, 18, 10, 10, 10, 18, 10, 18, 16, 16, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 18, 16, 16, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 10, 10, 10, 10, 10, 10, 10, 18, 10, 10, 10, 18, 10, 18, 16, 16, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 18, 16, 16, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 10, 10, 10, 18, 10, 18, 16, 16, 10, 18, 16, 16, 14, 14, 14, 14, 10, 18, 16, 16, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 10, 18, 16, 16, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 22, 12, 12, 12, 22, 12, 22, 20, 20, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 12, 12, 22, 12, 22, 20, 20, 12, 22, 20, 20, 18, 18, 18, 18, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 22, 20, 20, 18, 18, 18, 18, 16, 16, 16, 16, 16, 16, 16, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13];
b=[];for i=1:numel(stored)
a=dec2bin(i);
c=find(a=='1');
if numel(c)>=(numel(a)+1)/2
if mod(numel(a)+1,2)==1
b=[b numel(a)+1];
else
d=c((numel(a)+1)/2);
b=[b 2*d];
end
else
b=[b numel(a)+1];
end
end
for i=1:numel(stored)
if (b(i))
if b(i)~=stored(i)
'error',
end
end
end
which of is required ? 1 , 2, or 3 and how are our submissions scored – Abr001am – 2016-04-27T19:46:29.237
@Agawa001 "You can do that one of three ways:" Choose either one of them, whichever you think is easiest for the approach and language you want to use. – Martin Ender – 2016-04-27T19:47:19.243
Why all the repeating numbers today!?! http://codegolf.stackexchange.com/questions/78787/generate-n-digits-of-gijswijts-sequence :D
– cat – 2016-04-28T17:46:35.487