A073887 Smallest prime p such that sum of p and the next n-1 primes is a perfect square, or 1 if no such prime exists.

1, 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

Offset

1,2

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

Let p(k) be the k-th prime: p(1)=2, p(2)=3 etc. Define a(1)=1 and a(n)=p(k) such that p(k)+p(k+1)+...+p(k+n-1)=m^2 and there is no prime <p(k) such that this is true; or set a(n) = 0 if no such p(k) exists.

Example

a(5) = prime(42) = 181 because 181+191+193+197+199 = 961 = (31)^2.

Prog

(PARI) a(n) = {if (n==1, return (1)); forprime(p=2, , k = primepi(p); if (issquare(sum(i=k, k+n-1, prime(i))), return (p)); ); } \\ Michel Marcus, Dec 13 2014

Crossrefs

Sequence in context: A164064 A369490 A279232 * A132955 A217893 A063518

Adjacent sequences: A073884 A073885 A073886 * A073888 A073889 A073890

Keyword

nonn

Author

Amarnath Murthy, Aug 17 2002

Extensions

Edited and extended by Bruce Corrigan (scentman(AT)myfamily.com), Oct 20 2002

a(10) and a(21)-a(51) from Donovan Johnson, May 08 2010

Obsolete comment deleted by Zak Seidov, Dec 13 2014

Typo in Name fixed by Zak Seidov, Jul 07 2015

Status

approved