|
|
A284285
|
|
Numbers k such that (2^k + 3)/5 is prime.
|
|
0
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
For primes p = (2^a(n) + 3)/5, n >= 2, there are exactly 5 positive integers m for which the exponents of 2 and p in the prime power factorization of m! are both powers of 2 (for a proof see the Shevelev link (Theorem 2)).
The sequence of such primes p begins 7, 103, 6710887, 7036874417767, etc.
|
|
LINKS
|
|
|
FORMULA
|
a(n) == 1 (mod 4).
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more,changed
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|