A328264 a(n) is the least prime p such that prime(n) divides the sum of n consecutive primes starting with p.

2, 5, 2, 37, 83, 17, 7, 23, 13, 67, 163, 821, 227, 7, 13, 151, 599, 643, 271, 2, 83, 19, 83, 1069, 61, 37, 823, 263, 23, 857, 89, 1931, 139, 181, 71, 239, 1861, 739, 487, 37, 1237, 3833, 37, 6961, 1709, 499, 587, 271, 2687, 359, 5, 727, 73, 491, 73, 41, 3989, 797, 2083, 1451, 199, 349, 2027, 2441

Offset

1,1

Comments

a(n)=3 for n=850 and 55154 (and presumably infinitely many others).

Links

Robert Israel, Table of n, a(n) for n = 1..9332

Example

a(4)=37 because prime(4)=7 divides the sum of 4 consecutive primes starting with 37 (37+41+43+47=168), but does not divide any earlier sum of 4 consecutive primes.

Maple

P:= [0, seq(ithprime(i), i=1..100000)]:
S:= ListTools:-PartialSums(P):
f:= proc(n) local p, k;
  p:= ithprime(n);
  for k from 1 to nops(S)-n do
      if S[k+n]-S[k] mod p = 0 then
      return P[k+1]
      fi
    od;
  FAIL
end proc:
map(f, [$1..200]);

Mathematica

a[n_] := Block[{m=Prime@n, s=Sum[Prime@i, {i, n}], p=2, q}, q=m; While[Mod[s, m] > 0, s-=p; {p, q} = NextPrime@{p, q}; s+=q]; p]; Array[a, 70] (* Giovanni Resta, Oct 10 2019 *)

Crossrefs

Cf. A024011 (a(n)=2).

Sequence in context: A019295 A364820 A373146 * A170908 A229029 A055385

Adjacent sequences: A328261 A328262 A328263 * A328265 A328266 A328267

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 09 2019

Status

approved