This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345057 #8 Jun 07 2021 21:03:37
%S A345057 0,4,0,10,5,0,14,12,3,0,44,6,13,14,0,46,17,18,38,4,0,11,230,6,25,13,
%T A345057 90,0,29,10,62,40,33,34,70,0,37,57,39,20,41,28,86,4,0,23,1034,40,7,25,
%U A345057 102,78,53,9,0,28,114,145,1652,60,61,62,63,190,260,0,134,68,23,140,284,24,73,37,25,38,154,0
%N A345057 Distance to the next larger number k > n for which A011772(k) = A011772(n), or 0 if no such number exists.
%F A345057 a(n) = A345056(n) - n.
%o A345057 (PARI)
%o A345057 A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
%o A345057 A345057(n) = { my(x=A011772(n), y=binomial(x+1,2)); for(i=1+n,y,if(A011772(i)==x,return(i-n))); (0); };
%Y A345057 Cf. A000217 (positions of zeros), A002024, A011772, A066561, A345056, A345058.
%K A345057 nonn
%O A345057 1,2
%A A345057 _Antti Karttunen_, Jun 07 2021