A358156 a(n) is the smallest number k such that the sum of k consecutive prime numbers starting with the n-th prime is a square.

9, 23, 4, 1862, 14, 3, 2, 211, 331, 163, 366, 3, 124, 48, 2, 449, 8403, 121, 35, 2, 4, 105, 77, 43, 190769, 1726, 234, 248, 200, 295, 293, 73, 4, 873, 32, 64, 2456139382, 8, 4519, 14, 123, 5, 9395, 296, 26, 5, 3479, 810, 9, 7091, 1669, 157, 1189, 12559, 269, 4930, 21, 376, 3

Offset: 1

Author

Todor Szimeonov, Nov 01 2022

Keywords

• nonn

Comments

a(60) > 10^10 and a(68) > 10^13. - Martin Ehrenstein, Nov 09 2022

Examples

			For n=7, prime(7) = 17 and starting there 2 primes 17 + 19 = 36 which is square, so that a(7)=2.
		

Links

• Todor Szimeonov, Square of prime numbers

Crossrefs

Cf. A000040, A000290, A105720, A230327 (exchanges the roles of n, k), A287027 (squares reached).

Indices of terms: A064397 (2's), A076305 (3's), A072849 (4's), A166255 (70's), A166261 (120's).

Programs

Maple

f:= proc(n) local p,s,k;
  p:= ithprime(n); s:= p;
  for k from 2 do
    p:= nextprime(p);
    s:= s+p;
    if issqr(s) then return k fi
  od
end proc:
map(f, [$1..36]); # Robert Israel, Nov 08 2022

Mathematica

a[n_] := Module[{p = s = Prime[n], k = 1}, While[! IntegerQ[Sqrt[s]], p = NextPrime[p]; s += p; k++]; k]; Array[a, 36] (* Amiram Eldar, Nov 08 2022 *)

Extensions

a(25)-a(36) from Robert Israel, Nov 08 2022

a(37)-a(59) from Martin Ehrenstein, Nov 09 2022