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
Keywords
Examples
a(5) = prime(42) = 181 because 181+191+193+197+199 = 961 = (31)^2.
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000
Programs
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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
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
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