A218834 Primes p such that 3*p is greater than the greatest prime factor of p^3 - 1 and of p^3 + 1.

37, 47, 107, 211, 263, 373, 431, 521, 571, 631, 653, 719, 809, 821, 829, 941, 997, 1031, 1033, 1087, 1109, 1129, 1301, 1327, 1399, 1429, 1543, 1571, 1601, 1637, 1663, 1699, 1783, 1823, 1871, 1913, 1979, 1999, 2153, 2207, 2243, 2267, 2393, 2459, 2609, 2927

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

37^3 - 1 = 2^2*3^3*7*67, 37^3 + 1 = 2*19*31*43 and 37*3 > 43 and 37*3 > 67

Mathematica

Select[Prime[Range[PrimePi[3000]]], 3 # > FactorInteger[#^3 - 1][[-1, 1]] && 3 # > FactorInteger[#^3 + 1][[-1, 1]] &] (* T. D. Noe, Nov 07 2012 *)

Prog

(PARI) forprime(h=3, 5001, for(n=3, 3, 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: A159750 A108333 A231254 * A039465 A083240 A162556

Adjacent sequences: A218831 A218832 A218833 * A218835 A218836 A218837

Keyword

nonn

Author

Robin Garcia, Nov 07 2012

Status

approved