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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. 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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified November 28 17:22 EST 2022. Contains 358421 sequences. (Running on oeis4.)