A061890 Squares that are the sum of initial primes.

100, 25633969, 212372329, 292341604, 3672424151449, 219704732167875184222756

Offset

1,1

Comments

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

Links

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

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.

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A007504, A033997, A033998, A061888.

Cf. also A066527, A364691, A366269.

Sequence in context: A343182 A013855 A204576 * A333024 A126686 A279028

Adjacent sequences: A061887 A061888 A061889 * A061891 A061892 A061893

Keyword

nonn,more

Author

David W. Wilson, May 12 2001

Extensions

Corrected by Vladeta Jovovic, May 21 2001

a(6) from Giovanni Resta, May 27 2003

Edited by Ray Chandler, Mar 20 2007

Status

approved