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A284285 Numbers k such that (2^k + 3)/5 is prime. 0
5, 9, 25, 45, 61, 189, 289, 489, 7065, 42229 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..10.

V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236.

FORMULA

a(n) == 1 (mod 4).

MATHEMATICA

Select[Range[7500], PrimeQ[(2^# + 3)/5] &] (* Michael De Vlieger, Mar 24 2017 *)

PROG

(PARI) is(n)=n%4==1 && isprime((2^n+3)/5) \\ Charles R Greathouse IV, Mar 25 2017

CROSSREFS

Cf. A000040, A283657.

Sequence in context: A147074 A147192 A259665 * A025624 A147496 A147383

Adjacent sequences:  A284282 A284283 A284284 * A284286 A284287 A284288

KEYWORD

nonn,more

AUTHOR

Vladimir Shevelev, Mar 24 2017

EXTENSIONS

Terms a(4)-a(9) from Peter J. C. Moses, Mar 24 2017

a(10) from Giovanni Resta, Mar 24 2017

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)