A218833 Primes p such that 2*p is greater than the greatest prime factor of p^2 - 1 and p^2 + 1.

3, 7, 13, 17, 31, 41, 43, 47, 73, 83, 157, 173, 191, 193, 211, 233, 239, 241, 251, 269, 293, 307, 311, 313, 337, 401, 421, 431, 439, 443, 463, 467, 487, 491, 499, 509, 557, 563, 577, 593, 599, 601, 613, 647, 659, 691, 701, 743, 757, 787, 809, 811, 829, 853

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

3^2 - 1 = 2^3, 3^2 + 1 = 2*5 and 2*3 > 2 and 2*3 > 5
13^2 -1 = 2^3*3*7, 13^2 + 1 = 2*5*17 and 2*13 > 7 and 2*13 > 17

Mathematica

Select[Prime[Range[PrimePi[1000]]], 2 # > FactorInteger[#^2 - 1][[-1, 1]] && 2 # > FactorInteger[#^2 + 1][[-1, 1]] &] (* T. D. Noe, Nov 07 2012 *)

Prog

(PARI) forprime(h=3, 2001, for(n=2, 2, a=h^n; b=a-1; c=a+1; d=vecmax(factor(b)[, 1]~); e=vecmax(factor(c)[, 1]~); g=h*n; if(g>d && g>e, print1(h, ", "))))

Crossrefs

Sequence in context: A045422 A191071 A180543 * A113003 A045423 A214782

Adjacent sequences: A218830 A218831 A218832 * A218834 A218835 A218836

Keyword

nonn

Author

Robin Garcia, Nov 07 2012

Status

approved