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A218833
Primes p such that 2*p is greater than the greatest prime factor of p^2 - 1 and p^2 + 1.
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
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
KEYWORD
nonn
AUTHOR
Robin Garcia, Nov 07 2012
STATUS
approved