OFFSET
1,1
COMMENTS
Primes n such that n!*B(n+3) is an integer where B(k) are the Bernoulli numbers B(1) = -1/2, B(2) = 1/6, B(4) = -1/30, ..., B(2m+1) = 0 for m > 1.
If n is prime n!*B(n-1) is always an integer. Note that if Goldbach's conjecture (2n = p1 + p2 for all n >= 2) is false and K is the smallest value of n for which it fails, then for 2(K-2) = p3 + p4, the primes p3 and p4 must be taken from this list. See similar comment for A140555. - Keith Backman, Apr 06 2012
Complement of A023200 (primes p such that p + 4 is also prime) with respect to A000040 (primes). For p > 2: primes p such that there is no prime of the form r^2 + p where r is prime, subsequence of A232010. Example: the prime 7 is not in the sequence because 2^2 + 7 = 11 (prime). A232009(a(n)) = 0 for n > 1 . - Jaroslav Krizek, Nov 22 2013
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..1026
Eric Weisstein's World of Mathematics, Bernoulli Number
FORMULA
a(n) ~ n log n. - Charles R Greathouse IV, Nov 22 2013
MATHEMATICA
A067775 = {}; Do[p = Prime@ n; If[ IntegerQ[ p! BernoulliB[p + 3]], AppendTo[A067775, p]], {n, 77}]; A067775 (* Robert G. Wilson v, Aug 19 2008 *)
Select[Prime[Range[80]], Not[PrimeQ[# + 4]] &] (* Alonso del Arte, Apr 02 2014 *)
PROG
(PARI) lista(nn) = {forprime(p=1, nn, if (! isprime(p+4), print1(p, ", ")); ); } \\ Michel Marcus, Nov 22 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 06 2002
EXTENSIONS
New name from Klaus Brockhaus at the suggestion of Michel Marcus, Nov 22 2013
STATUS
approved