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A267123
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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.
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2
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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)
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MATHEMATICA
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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 *)
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PROG
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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