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A033998 Numbers n such that the sum of the primes <= n is a square. 3
23, 22073, 67187, 79427, 10729219, 3531577135439 (list; graph; refs; listen; history; text; internal format)
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: A090674 A013728 A028693 * A157167 A233210 A173369

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

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Last modified August 28 20:13 EDT 2015. Contains 261164 sequences.