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

Author

Enoch Haga, Sep 06 2007

Keywords

• easy
• nonn

Comments

Essentially the same as A073887.

Examples

			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.
		

Links

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

Crossrefs

Cf. A132956, A132957.

Programs

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 *)

PARI

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

Formula

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

Extensions

Edited by R. J. Mathar, Nov 27 2007