A267125 Numbers n such that n+2!, n+2!+3!, n+2!+3!+4!, n+2!+3!+4!+5!, n+2!+3!+4!+5!+6!, n+2!+3!+4!+5!+6!+7!, n+2!+3!+4!+5!+6!+7!+8!, n+2!+3!+4!+5!+6!+7!+8!+9!, and n+2!+3!+4!+5!+6!+7!+8!+9!+10! are all prime.

3525, 58755, 2171625, 3711201, 4612811, 4657289, 6714495, 7075271, 7687071, 9330381, 10523045, 11904249, 14060501, 16634171, 17191839, 22909971, 32351711, 35723709, 43992879, 45377325, 49031165, 56682171, 60219615, 64348635, 83743601, 86669615, 94265805

Offset: 1

Author

Emre APARI, Jan 10 2016

Keywords

• nonn

Examples

			3525+2!=3527 (is prime)
3525+2!+3!=3533 (is prime)
3525+2!+3!+4!=3557 (is prime)
3525+2!+3!+4!+5!=3677 (is prime)
3525+2!+3!+4!+5!+6!=4397 (is prime)
3525+2!+3!+4!+5!+6!+7!=9437 (is prime)
3525+2!+3!+4!+5!+6!+7!+8!=49757 (is prime)
3525+2!+3!+4!+5!+6!+7!+8!+9!=412637 (is prime)
3525+2!+3!+4!+5!+6!+7!+8!+9!+10!=4041437 (is prime)
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054116, A267123.

Programs

Mathematica

r = Accumulate@ Array[#! &, 9, 2]; fQ[n_] := Union[ PrimeQ[n + r]] == {True}; k = 1; lst = {}; While[k < 10^8, If[ fQ@ k, AppendTo[lst, k]]; k += 2]; lst (* Robert G. Wilson v, Jan 10 2016 *)

PARI

is(n)=for(k=2,10,if(!isprime(n+=k!), return(0))); 1 \\ Charles R Greathouse IV, Feb 23 2016

PARI

list(lim)=my(v=List(),p=2,q=3,g,n); forprime(r=5,lim+8, g=q-p; if(g>6 || (g<6 && r-p>6), p=q;q=r; next); n=p+6; for(k=4,10, if(!isprime(n+=k!), p=q;q=r;next(2))); listput(v,p-2);p=q;q=r); Vec(v) \\ Charles R Greathouse IV, Feb 23 2016

Extensions

a(11) onward from Robert G. Wilson v, Jan 10 2016