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

Author

Balarka Sen, May 12 2012

Keywords

• nonn
• easy

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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!
1))  \\ M. F. Hasler, May 20 2012