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 A218394 #16 Aug 14 2025 01:09:19
%S A218394 1,5,7,11,25,27,31,35,37,51,55,57,61,125,127,131,135,137,151,155,157,
%T A218394 161,175,177,181,185,187,251,255,257,261,275,277,281,285,287,301,305,
%U A218394 307,311,625,627,631,635,637,651,655,657,661,675,677,681,685,687,751
%N A218394 Numbers such that sum(i<=n) binomial(n,i)*binomial(2*n-2*i, n-i) is not divisible by 5.
%C A218394 a(n) = A037453(2*n-1) (proved by Schur, see link).
%H A218394 W. Shur, <a href="https://doi.org/10.37236/1331">The last digit of C(2*n,n) and Sigma C(n,i)*C(2*n-2*i,n-i)</a>, The Electronic Journal of Combinatorics, #R16, Volume 4, Issue 2 (1997).
%F A218394 a(n) = 2*n - 1 + 2*sum{i=1,n} 5^(i-1)*floor((2*n-1)/3^i).
%o A218394 (PARI) lista(nb) = {for (n=1, nb, if (sum(i=1,n, binomial(n, i)*binomial(2*n-2*i,n-i)) % 5 != 0, print1(n, ", ")););}
%o A218394 (PARI) a(n) = {2*n-1+2*sum(i=1,n, 5^(i-1)*floor((2*n-1)/3^i))}
%o A218394 (Python)
%o A218394 from gmpy2 import digits
%o A218394 def A218394(n): return int(digits((n<<1)-1,3),5) # _Chai Wah Wu_, Aug 10 2025
%Y A218394 Cf. A037453.
%K A218394 nonn
%O A218394 1,2
%A A218394 _Michel Marcus_, Oct 28 2012