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 A263549 #15 Jun 03 2024 03:48:05
%S A263549 1,3,67,141,2201,2625,8153,10187,11089,136515,138377,1543419,1712109,
%T A263549 5097739,51562297,1459124841,42825210689
%N A263549 Numbers k such that k divides the sum of the first k primes with odd indices.
%C A263549 a(n) is always an odd number since the first prime is 2.
%C A263549 How do a(n) and A263546(n) compare asymptotically?
%e A263549 1 is in the sequence because prime(1) = 2 is divisible by 1.
%e A263549 3 is in the sequence because prime(1) + prime(3) + prime(5) = 2 + 5 + 11 = 18 is divisible by 3.
%t A263549 Select[Range@ 10000, Divisible[Sum[Prime[2 i - 1], {i, 1, #}], #] &] (* _Michael De Vlieger_, Oct 21 2015 *)
%o A263549 (PARI) list(lim)=my(v=List(), k, s, t); forprime(p=2, , if((t++) && t%2==1, s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v)))))
%Y A263549 Cf. A045345, A077131, A263541, A263546.
%K A263549 nonn,more
%O A263549 1,2
%A A263549 _Altug Alkan_, Oct 21 2015
%E A263549 a(17) from _Amiram Eldar_, Jun 03 2024