A267123 - OEIS

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

(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

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)

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 *)

PROG

(PARI) is(n)=for(k=2, 7, 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, 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

CROSSREFS

Cf. A054116, A267125.

Sequence in context: A219389 A373443 A217085 * A115779 A147339 A147377

Adjacent sequences: A267120 A267121 A267122 * A267124 A267125 A267126

KEYWORD

nonn

AUTHOR

Emre APARI, Jan 10 2016

STATUS

approved