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

1,1

Links

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

Example

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)

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 *)

Prog

(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

Crossrefs

Cf. A054116, A267123.

Sequence in context: A185920 A264450 A187726 * A241240 A035897 A064256

Adjacent sequences: A267122 A267123 A267124 * A267126 A267127 A267128

Keyword

nonn

Author

Emre APARI, Jan 10 2016

Extensions

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

Status

approved