A139023 Smallest prime factor of n! + 2^n - 1.

2, 5, 13, 3, 151, 3, 5167, 3, 7, 3, 39918847, 3, 17, 3, 7, 3, 829, 3, 25561, 3, 7, 3, 929, 3, 67, 3, 7, 3, 37, 3, 941, 3, 7, 3, 31, 3, 47, 3, 7, 3, 839, 3, 167, 3, 7, 3, 101, 3, 859, 3, 7, 3, 165437, 3, 23, 3, 7, 3, 199, 3, 526588200926847656291, 3, 7, 3, 31, 3, 157, 3, 7, 3

Offset

1,1

Links

K. Brockhaus, Table of n, a(n) for n = 1..108.

Florian Luca and Igor E. Shparlinski, On the largest prime factor of n! + 2^n - 1, Journal de Theorie des Nombres de Bordeaux 17 (2005), 859-870.

Maple

# this code will produce FAIL for terms that can't be computed within a
# 30 second time limit
spf:= proc(n) local F;
F:= select(f -> f[1]::integer, ifactors(n, easy)[2]);
if F = [] then F:= traperror(timelimit(30, ifactors(n)[2])) fi;
if F = lasterror then FAIL else min(seq(f[1], f=F)) fi
end proc:
seq(spf(n!+2^n-1), n=1..100); # Robert Israel, Sep 18 2016

Mathematica

a = {}; Do[AppendTo[a, n! + 2^n - 1], {n, 1, 40}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[1]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b
Table[FactorInteger[n! + 2^n - 1] [[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Sep 18 2016 *)

Prog

(Magma) trialdiv:=function(n, P) val:=0; for p in P do if n mod p eq 0 then val:=p; break; end if; end for; return val; end function; P:=PrimesUpTo(300000000); [ trialdiv(a, P) where a is Factorial(n)+2^n-1: n in [1..70] ]; //a(61) requires a separate computation. // Klaus Brockhaus, Nov 06 2009
(PARI) a(n)=factor(n!+2^n-1)[1, 1] \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A127986, A127987, A139024.

Sequence in context: A135329 A114508 A243366 * A241758 A173620 A319920

Adjacent sequences: A139020 A139021 A139022 * A139024 A139025 A139026

Keyword

nonn

Author

Artur Jasinski, Apr 06 2008, corrected Apr 22 2008

Extensions

a(1) - a(40) verified and a(41) - a(70) added by Klaus Brockhaus, Nov 06 2009

Status

approved