VOOZH about

URL: https://oeis.org/A212266

⇱ A212266 - OEIS

login
A212266
Primes p such that p - m! is composite, where m is the greatest number such that m! < p.
4
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
KEYWORD
nonn,easy
AUTHOR
Balarka Sen, May 12 2012
STATUS
approved