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A092789
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a(n) = smallest prime of the form prime(n)+m! for some m >= 0.
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4
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3, 5, 7, 13, 13, 19, 19, 43, 29, 31, 37, 43, 43, 67, 53, 59, 61, 67, 73, 73, 79, 103, 89, 113, 103, 103, 109, 109, 229, 137, 151, 137, 139, 163, 151, 157, 163, 283, 173, 179, 181, 363061, 193, 199, 199, 223, 331, 229, 229, 349, 239, 241, 5281, 257, 263, 269, 271
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OFFSET
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1,1
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COMMENTS
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n! + p is composite for n >= p since p divides n! for n >= p.
Is it known that such a prime always exists? If not the definition should say "or -1 if no such prime exists". - N. J. A. Sloane, Aug 11 2011
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LINKS
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MAPLE
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A092789 := proc(n) local q, m ; for m from 0 do q := ithprime(n)+m! ; if isprime(q) then return q; end if; end do ; end proc:
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PROG
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(PARI) nfactpm3(n) = { forprime(p=1, n, c=0; for(x=0, n, y=x!+p; if(isprime(y), c++; print1(y", "); break)); ) }
(Magma) SmallestP:=function(p) for m in [0..p-1] do q:=p+Factorial(m); if IsPrime(q) then return q; end if; end for; return -1; end function; [ SmallestP(NthPrime(n)): n in [1..80] ]; // Klaus Brockhaus, Mar 02 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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