A033998 Numbers n such that the sum of the primes <= n is a square.

23, 22073, 67187, 79427, 10729219, 3531577135439

Offset

1,1

Links

Table of n, a(n) for n=1..6.

G. L. Honaker Jr. and C. Caldwell, Prime Curios!: 9

G. L. Honaker Jr. and C. Caldwell, Prime Curios!: 3531577135439

C. Riveras, PrimePuzzles.Net, Problem 9: Sum of first k primes is perfect square

Formula

a(n) = Prime(A033997(n))

Example

2+3+5+7+11+13+17+19+23 = 10^2 is a square, so 23 is in the sequence.

Mathematica

Prime[#]&/@Flatten[Position[Accumulate[Prime[Range[710000]]], _?(IntegerQ[ Sqrt[#]]&)]] (* This program will generate the first 5 terms of the sequence. *) (* Harvey P. Dale, Jun 22 2013 *)

Prog

(PARI) s=0; forprime(p=2, 1e6, if(issquare(s+=p), print1(p", "))) \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A000040, A033997, A061888, A061890.

Sequence in context: A324255 A273940 A348307 * A157167 A273192 A233210

Adjacent sequences: A033995 A033996 A033997 * A033999 A034000 A034001

Keyword

nonn

Author

Calculated by Jud McCranie

Extensions

3531577135439 from Giovanni Resta, May 27 2003

Edited by Ray Chandler, Mar 20 2007

Status

approved