

A073887


Smallest prime p such that sum of p and the next n1 primes is a perfect square, or 1 if no such prime exists.


2



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
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OFFSET

1,2


LINKS

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


FORMULA

Let p(k) be the kth 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+n1)=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+n1, prime(i))), return (p)); ); } \\ Michel Marcus, Dec 13 2014


CROSSREFS

Sequence in context: A040274 A164064 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



