

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
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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+n1) 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+n1, 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



