A085747 Least positive k such that n! + k is a semiprime.
3, 2, 3, 1, 1, 1, 1, 1, 5, 1, 3, 17, 1, 1, 7, 2, 3, 23, 1, 1, 11, 29, 3, 1, 1, 1, 37, 1, 41, 2, 19, 11, 11, 1, 7, 3, 41, 1, 13, 127, 47, 59, 2, 37, 5, 37, 59, 1, 2, 73, 59, 79, 73, 1, 1, 61, 118, 37, 1, 61, 31, 37, 43, 7, 83, 71, 19, 7, 103, 19, 1, 107, 37, 167, 1, 103, 3, 73, 109, 97
Offset: 1
Links
- Tyler Busby, Table of n, a(n) for n = 1..107 (terms 1..99, 101..103, and 105 from Max Alekseyev, terms 100 and 104 from Sean A. Irvine)
- Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
- factordb, Status of 106!+139.
- Hisanori Mishima, Factorization of n! + 1 (n = 1 to 100)
Programs
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Magma
m:=1; sol:=[]; for n in [1..40] do k:=1; while &+[d[2]: d in Factorization(Factorial(n)+k)] ne 2 do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Aug 24 2019
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Mathematica
Table[SelectFirst[Range@ 1000, PrimeOmega[n! + #] == 2 &], {n, 40}] (* Michael De Vlieger, Mar 08 2016, Version 10 *) lpk[n_]:=Module[{k=1,fn=n!},While[PrimeOmega[fn+k]!=2,k++];k]; Array[lpk,80] (* Harvey P. Dale, Feb 18 2025 *) -
PARI
a(n) = {k = 1; while (bigomega(n!+k) != 2, k++); k;} \\ Michel Marcus, Mar 08 2016
Extensions
Extended by Robert G. Wilson v, Jul 27 2003
a(55) from Ray Chandler, Nov 09 2003
a(56)-a(80) from Sean A. Irvine, Mar 29 2010
Comments