

A082470


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


4



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, 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, 13, 11, 9, 19, 12, 13, 16, 11, 19, 17, 9, 13
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OFFSET

2,1


COMMENTS

k! + p is composite for k >= p since p divides k! for k >= p.
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]
Apparently it is not known whether a(n) is ever zero.  N. J. A. Sloane, Aug 11 2011


LINKS

Table of n, a(n) for n=2..67.


EXAMPLE

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


MAPLE

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;


MATHEMATICA

Table[Count[Range[0, Prime[n]1]!+Prime[n], _?PrimeQ], {n, 70}] (* Harvey P. Dale, Feb 06 2019 *)


PROG

(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


CROSSREFS

Cf. A092789, A175193, A175194.
Sequence in context: A117407 A232095 A279436 * A101204 A169808 A283069
Adjacent sequences: A082467 A082468 A082469 * A082471 A082472 A082473


KEYWORD

nonn,more


AUTHOR

Jeff Burch, Apr 27 2003


EXTENSIONS

Edited by Franklin T. AdamsWatters, Aug 01 2006


STATUS

approved



