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%I #21 Feb 26 2016 13:10:56
%S 3525,58755,2171625,3711201,4612811,4657289,6714495,7075271,7687071,
%T 9330381,10523045,11904249,14060501,16634171,17191839,22909971,
%U 32351711,35723709,43992879,45377325,49031165,56682171,60219615,64348635,83743601,86669615,94265805
%N 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.
%H Charles R Greathouse IV, <a href="/A267125/b267125.txt">Table of n, a(n) for n = 1..10000</a>
%e 3525+2!=3527 (is prime)
%e 3525+2!+3!=3533 (is prime)
%e 3525+2!+3!+4!=3557 (is prime)
%e 3525+2!+3!+4!+5!=3677 (is prime)
%e 3525+2!+3!+4!+5!+6!=4397 (is prime)
%e 3525+2!+3!+4!+5!+6!+7!=9437 (is prime)
%e 3525+2!+3!+4!+5!+6!+7!+8!=49757 (is prime)
%e 3525+2!+3!+4!+5!+6!+7!+8!+9!=412637 (is prime)
%e 3525+2!+3!+4!+5!+6!+7!+8!+9!+10!=4041437 (is prime)
%t 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 *)
%o (PARI) is(n)=for(k=2,10,if(!isprime(n+=k!), return(0))); 1 \\ _Charles R Greathouse IV_, Feb 23 2016
%o (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
%Y Cf. A054116, A267123.
%K nonn
%O 1,1
%A _Emre APARI_, Jan 10 2016
%E a(11) onward from _Robert G. Wilson v_, Jan 10 2016
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