A218849 Primes p such that 4*p is greater than the greatest prime factor of p^4 -1 and p^4 + 1.

2383, 3373, 10181, 11483, 18979, 30727, 35677, 35837, 37783, 41879, 41893, 47041, 48131, 49253, 53309, 55541, 62497, 67103, 84229, 88607, 91499, 95869, 97397, 99523, 104161, 105557, 107747, 113149, 118493, 118927, 137339, 145501, 146291, 148153, 149713, 165701

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

2383^4 - 1 = 2^6*3*5*149*157*397*3617, 2383^4 + 1 = 2*809*857*2833*8209 and 4*2383 > 8209 and 4*2383 > 3617.

Mathematica

Select[Prime[Range[PrimePi[200000]]], 4 # > FactorInteger[#^4 - 1][[-1, 1]] && 4 # > FactorInteger[#^4 + 1][[-1, 1]] &] (* T. D. Noe, Nov 07 2012 *)

Prog

(PARI) forprime(h=3, 200001, for(n=4, 4, 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: A107530 A020394 A251649 * A254562 A186867 A210078

Adjacent sequences: A218846 A218847 A218848 * A218850 A218851 A218852

Keyword

nonn

Author

Robin Garcia, Nov 07 2012

Status

approved