A061890 Squares that are the sum of initial primes.

100, 25633969, 212372329, 292341604, 3672424151449, 219704732167875184222756

Offset: 1

Author

David W. Wilson, May 12 2001

Keywords

• nonn
• more

Comments

The set of squares in A007504. - Zak Seidov, Oct 07 2015

Examples

			100 = 10^2 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23, so 100 is in the sequence.
		

Links

• G. L. Honaker Jr. and C. Caldwell, Prime Curios!: 9
• Carlos Rivera, Problem 9: Sum of first k primes is perfect square, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A007504, A033997, A033998, A061888.

Cf. also A066527, A364691, A366269.

Programs

Maple

N:= 10^7: # to use primes up to N
P:= select(isprime, [2,seq(2*i+1, i=1..floor(N/2))]):
S:= ListTools:-PartialSums(P):
select(issqr,S); # Robert Israel, Feb 16 2015

Mathematica

s[n_] := Sum[Prime[i], {i, 1, n}];t := Table[s[n], {n, 20000}];Select[t, IntegerQ[Sqrt[#]] &] (* Carlos Eduardo Olivieri, Feb 24 2015 *)

PARI

lista() = {s = 0; forprime(p=2, ,s += p; if (issquare(s), print1(s, ", ")););} \\ Michel Marcus, Mar 10 2015

Formula

a(n) = A061888(n)^2.

Intersection of A000290 and A007504. - Zak Seidov, Oct 08 2015

Extensions

Corrected by Vladeta Jovovic, May 21 2001

a(6) from Giovanni Resta, May 27 2003

Edited by Ray Chandler, Mar 20 2007