A212266 Primes p such that p - m! is composite, where m is the greatest number such that m! < p.

59, 73, 79, 89, 101, 109, 197, 211, 239, 241, 263, 281, 307, 337, 367, 373, 379, 409, 419, 421, 439, 443, 449, 461, 463, 491, 523, 547, 557, 571, 593, 601, 613, 617, 631, 647, 653, 659, 673, 701, 709, 769, 797, 811, 839, 853, 863, 881, 907, 929, 937, 941, 967

Offset

1,1

Comments

The first five terms 59, 73, 79, 89, 101 belong to A023209. The terms 409, 419, 421, 439, 443, 449 also belong to A127209.

It seems likely that a(n) ~ n log n, can this be proved? - Charles R Greathouse IV, Sep 20 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

29 is not a member because 29 - 4! = 5 is prime.
59 is a member because 59 - 4! = 35 is composite.

Mathematica

Select[Prime[Range[200]], Module[{m=9}, CompositeQ[While[m!>=#, m--]; #-m!]]&] (* The initial m constant (set at 9 in the program) needs to be increased if the prime Range constant (set at 200 in the program) is increased beyond 30969. *) (* Harvey P. Dale, Dec 01 2023 *)

Prog

(PARI) for(n=3, 5, N=n!; forprime(p=N+3, N*(n+1), if(!isprime(p-N), print1(p", ")))) \\ Charles R Greathouse IV, May 12 2012
(PARI) is_A212266(p)=isprime(p) && for(n=1, p, n!<p || return(bigomega(p-(n-1)!)>1))  \\ M. F. Hasler, May 20 2012

Crossrefs

Cf. A212600, A212598, A136437, A023209, A127209.

Sequence in context: A139938 A033235 A106913 * A322919 A026050 A347804

Adjacent sequences: A212263 A212264 A212265 * A212267 A212268 A212269

Keyword

nonn,easy

Author

Balarka Sen, May 12 2012

Status

approved