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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 23 13:37 EST 2020. Contains 331171 sequences. (Running on oeis4.)