A132955 Smallest prime in a sequence of n consecutive primes which add to a perfect square.

17, 13, 5, 181, 587, 13, 163, 2, 13789, 1013, 163, 653, 11, 3931, 397, 2039, 439, 4447, 1217, 269, 1733, 3, 5, 2239, 197, 3, 1061, 14563, 1901, 3, 149, 359, 2137, 67, 433, 11, 907, 2339, 673, 19181, 11593, 89, 6883, 3, 28571, 997, 43, 3559, 2287, 1931, 911

Offset

2,1

Comments

Essentially the same as A073887.

Links

Zak Seidov, Table of n, a(n) for n = 2..1000

Formula

a(n)={ min prime(k): [ sum(j=k..k+n-1) prime(j)] in A000290}. - R. J. Mathar, Nov 27 2007

Example

a(2)=17, because it is the smallest prime in a sequence of n=2 consecutive primes, which add to a perfect square, namely 17+19=36=6^2. The sums of earlier pairs, 2+3, 3+5, 5+7, 7+11 etc. fail to produces sums which are any perfect square.

Mathematica

Module[{prs=Prime[Range[3200]]}, Table[First[SelectFirst[Partition[ prs, n, 1], IntegerQ[ Sqrt[Total[#]]]&]], {n, 2, 52}]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Sep 06 2015 *)

Prog

(PARI) a(n) = {ip = 1; while (! issquare(sum(i=ip, ip+n-1, prime(i))), ip++); prime(ip); } \\ Michel Marcus, Jun 08 2014

Crossrefs

Cf. A132956, A132957.

Sequence in context: A369490 A279232 A073887 * A217893 A063518 A168250

Adjacent sequences: A132952 A132953 A132954 * A132956 A132957 A132958

Keyword

easy,nonn

Author

Enoch Haga, Sep 06 2007

Extensions

Edited by R. J. Mathar, Nov 27 2007

Status

approved