A218863 Smallest prime p such that n*p is greater than the greatest prime factors of p^n - 1 and of p^n + 1.

3, 3, 37, 2383, 69011, 4027

Offset

1,1

Comments

a(7) > 4000000. - T. D. Noe, Nov 08 2012

Links

Table of n, a(n) for n=1..6.

Example

4027^6 - 1 = 2^3*3^2*7*11*13*19*53*61*229*709*1759*3373,
4027^6 + 1 = 2*5*37*41*1069*1381*1993*9733*9817,
and 6*4027 > 3373 and 6*4027 > 9817,
3^1 - 1 = 2, 3^1 + 1 = 2^2 and 3 > 2.

Maple

A218863 := proc(n)
    p := 2 ;
    for i from 1 do
        max(op(numtheory[factorset](p^n-1))) ;
        if n*p > % then
            max(op(numtheory[factorset](p^n+1))) ;
            if n*p > % then
                return p;
            end if;
        end  if;
        p := nextprime(p) ;
    end do:
end proc: # R. J. Mathar, Nov 07 2012

Mathematica

Table[p = 2; While[n*p <= FactorInteger[p^n - 1][[-1, 1]] || n*p <= FactorInteger[p^n + 1][[-1, 1]], p = NextPrime[p]]; p, {n, 6}] (* T. D. Noe, Nov 07 2012 *)

Crossrefs

Sequence in context: A206477 A372022 A219210 * A082394 A308645 A086889

Adjacent sequences: A218860 A218861 A218862 * A218864 A218865 A218866

Keyword

nonn

Author

Robin Garcia, Nov 07 2012

Status

approved