

A164571


Numbers n such that n and n+3 are prime powers.


6



1, 2, 4, 5, 8, 13, 16, 29, 61, 64, 125, 128, 509, 1021, 4093, 4096, 16381, 32768, 65536, 262144, 1048573, 4194301, 16777213, 268435456, 536870909, 1073741824, 36028797018963968
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OFFSET

1,2


COMMENTS

Numbers n such that n + (0, 3) is a prime power pair.
n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
n + (0, 2m1), m >= 1, being a nonadmissible pattern for prime pairs, since (0, 2m1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a  2m1, 2^a) or (2^a, 2^a + 2m1), a >= 0.]
n + (0, 3) being a nonadmissible pattern for prime pairs, has only prime power pairs (2^a  3, 2^a) or (2^a, 2^a + 3), a >= 0.
Numbers n such that n and n+3 are primes would give only 2, for the prime pair (2, 5).
10^18 < a(28) <= 19807040628566084398385987581.  Donovan Johnson, Aug 17 2009


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..50


PROG

(PARI) ispp(n) = (n==1)  isprime(n)  (ispower(n, , &p) && isprime(p));
isok(n) = ispp(n) && ispp(n+3); \\ Michel Marcus, Aug 31 2013
(PARI) v=List(); for(n=0, 1e3, if(isprimepower(2^n3), listput(v, 2^n3)); if(isprimepower(2^n+3), listput(v, 2^n))); Set(v) \\ Charles R Greathouse IV, Apr 24 2015


CROSSREFS

Cf. A000961.
Cf. A006549 Numbers n such that n and n+1 are prime powers.
Cf. A120431 Numbers n such that n and n+2 are prime powers.
Cf. A164571 Numbers n such that n and n+3 are prime powers.
Cf. A164572 Numbers n such that n and n+4 are prime powers.
Cf. A164573 Numbers n such that n and n+5 are prime powers.
Cf. A164574 Numbers n such that n and n+6 are prime powers.
Sequence in context: A294944 A178656 A085443 * A238589 A288668 A264800
Adjacent sequences: A164568 A164569 A164570 * A164572 A164573 A164574


KEYWORD

nonn


AUTHOR

Daniel Forgues, Aug 16 2009


EXTENSIONS

Edited by Daniel Forgues, Aug 17 2009
a(20)a(27) from Donovan Johnson, Aug 17 2009


STATUS

approved



