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A218863 Smallest prime p such that n*p is greater than the greatest prime factors of p^n - 1 and of p^n + 1. 2
3, 3, 37, 2383, 69011, 4027 (list; graph; refs; listen; history; text; internal format)
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: A303820 A206477 A219210 * A082394 A308645 A086889

Adjacent sequences:  A218860 A218861 A218862 * A218864 A218865 A218866

KEYWORD

nonn

AUTHOR

Robin Garcia, Nov 07 2012

STATUS

approved

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Last modified September 21 11:18 EDT 2019. Contains 327253 sequences. (Running on oeis4.)