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A212266
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Primes p such that p - m! is composite, where m is the greatest number such that m! < p.
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4
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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
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1,1
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COMMENTS
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The first five terms 59, 73, 79, 89, 101 belong to A023209. The terms 409, 419, 421, 439, 443, 449 also belong to A127209.
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LINKS
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EXAMPLE
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29 is not a member because 29 - 4! = 5 is prime.
59 is a member because 59 - 4! = 35 is composite.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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