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A061890 Squares that are the sum of initial primes. 5
100, 25633969, 212372329, 292341604, 3672424151449, 219704732167875184222756 (list; graph; refs; listen; history; text; internal format)
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

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

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.

Sequence in context: A265720 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

219704732167875184222756 from Giovanni Resta, May 27 2003

Edited by Ray Chandler, Mar 20 2007

STATUS

approved

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Last modified September 26 11:45 EDT 2020. Contains 337370 sequences. (Running on oeis4.)