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A132955 Smallest prime in a sequence of n consecutive primes which add to a perfect square. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A164064 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

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Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)