A267123 Integers n such that n+2!, n+2!+3!, n+2!+3!+4!, n+2!+3!+4!+5!, n+2!+3!+4!+5!+6!, and n+2!+3!+4!+5!+6!+7! are all prime.
11, 15, 99, 231, 351, 455, 725, 3525, 4935, 5405, 5709, 7575, 7641, 12545, 12891, 13749, 16065, 19859, 20475, 23969, 27791, 28049, 28571, 42459, 54615, 58755, 61979, 64481, 71835, 81011, 86261, 88649
Offset: 1
Keywords
Examples
99+2!=101 (is prime) 99+2!+3!=107 (is prime) 99+2!+3!+4!=131 (is prime) 99+2!+3!+4!+5!=251 (is prime) 99+2!+3!+4!+5!+6!=971 (is prime) 99+2!+3!+4!+5!+6!+7!=6011 (is prime)
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
r = {2, 8, 32, 152, 872, 5912}; fQ[n_] := Union[ PrimeQ[n + r]] == {True}; Select[ Range@ 100000, fQ] (* Robert G. Wilson v, Jan 10 2016 *) -
PARI
is(n)=for(k=2,7,if(!isprime(n+=k!), return(0))); 1 \\ Charles R Greathouse IV, Feb 23 2016
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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=4,7, 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