

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
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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.


PROG

(PARI) for(n=3, 5, N=n!; forprime(p=N+3, N*(n+1), if(!isprime(pN), print1(p", ")))) \\ Charles R Greathouse IV, May 12 2012
(PARI) is_A212266(p)=isprime(p) && for(n=1, p, n!<p  return(bigomega(p(n1)!)>1)) \\ M. F. Hasler, May 20 2012


CROSSREFS

Cf. A212600, A212598, A136437, A023209, A127209.
Sequence in context: A139938 A033235 A106913 * A322919 A026050 A304356
Adjacent sequences: A212263 A212264 A212265 * A212267 A212268 A212269


KEYWORD

nonn,easy


AUTHOR

Balarka Sen, May 12 2012


STATUS

approved



