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A082470 Number of k >= 0 such that k! + prime(n) is prime. 4

%I

%S 2,1,3,4,5,3,6,7,6,6,9,11,9,5,10,9,10,9,9,8,9,9,11,8,10,10,12,16,12,

%T 10,10,13,14,14,16,11,12,9,15,10,9,8,12,9,10,6,8,7,14,13,10,21,15,9,

%U 13,11,9,19,12,13,16,11,19,17,9,13

%N Number of k >= 0 such that k! + prime(n) is prime.

%C k! + p is composite for k >= p since p divides k! for k >= p.

%C The first 10^6 terms are nonzero. Remarkably, the number 7426189+m! is composite for all m <= 1793. [From _T. D. Noe_, Mar 02 2010]

%C Apparently it is not known whether a(n) is ever zero. - _N. J. A. Sloane_, Aug 11 2011

%e For n = 4, 3!+7 = 13, 4!+7=31, 5!+7=127 and 6!+7 = 727 are the 4 primes in n!+7

%p for i from 2 to 50 do ctr := 0: for j from 2 to ithprime(i)-1 do if isprime(j!+ithprime(i))=true then ctr := ctr+1 fi od; print(ctr); od;

%t Table[Count[Range[0,Prime[n]-1]!+Prime[n],_?PrimeQ],{n,70}] (* _Harvey P. Dale_, Feb 06 2019 *)

%o (PARI) nfactppct(n) = { forprime(p=1,n, c=0; for(x=0,n,y=x!+p;if(isprime(y),c++) ); print1(c",") ) } - _Cino Hilliard_, Apr 15 2004

%Y Cf. A092789, A175193, A175194.

%K nonn,more

%O 2,1

%A _Jeff Burch_, Apr 27 2003

%E Edited by _Franklin T. Adams-Watters_, Aug 01 2006

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)