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 A263549 Numbers k such that k divides the sum of the first k primes with odd indices. 0
 1, 3, 67, 141, 2201, 2625, 8153, 10187, 11089, 136515, 138377, 1543419, 1712109, 5097739, 51562297, 1459124841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is always an odd number since the first prime is 2. How do a(n) and A263546(n) compare asymptotically? LINKS EXAMPLE 1 is in the sequence because prime(1) = 2 is divisible by 1. 3 is in the sequence because prime(1) + prime(3) + prime(5) = 2 + 5 + 11 = 18 is divisible by 3. MATHEMATICA Select[Range@ 10000, Divisible[Sum[Prime[2 i - 1], {i, 1, #}], #] &] (* Michael De Vlieger, Oct 21 2015 *) PROG (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))))) CROSSREFS Cf. A045345, A077131, A263541, A263546. Sequence in context: A142035 A142926 A041983 * A225191 A201857 A294395 Adjacent sequences:  A263546 A263547 A263548 * A263550 A263551 A263552 KEYWORD nonn,more AUTHOR Altug Alkan, Oct 21 2015 STATUS approved

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Last modified January 19 20:48 EST 2022. Contains 350466 sequences. (Running on oeis4.)