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