A164512 -id:A164512 - cp's OEIS frontend

A264747 Prime powers n such that either n - 1 or n + 1 is a prime power, but not both.

1, 5, 7, 9, 16, 17, 31, 32, 127, 128, 256, 257, 8191, 8192, 65536, 65537, 131071, 131072, 524287, 524288, 2147483647, 2147483648, 2305843009213693951, 2305843009213693952, 618970019642690137449562111

Offset: 1

Juri-Stepan Gerasimov, Nov 23 2015

nonn

From Robert Israel, Nov 25 2015: (Start)
By Mihailescu's theorem, the only case where n-1 and n are both in A025475 is n=9. Thus for n > 9 the sequence consists of the following:
     n = 2^p - 1 and 2^p where 2^p-1 is a Mersenne prime (A000668);
     n = 2^(2^m) and 2^(2^m)+1 where 2^(2^m)+1 is a Fermat prime (A019434).
(End)

			7 is in this sequence because 7 and 7 + 1 = 8 are both prime power, but 7 - 1 = 6 is not a prime power.

Robert Israel, Table of n, a(n) for n = 1..42

Cf. A000668, A000961, A019434, A164512, A174269.

fermats:= {seq(2^(2^m)+1, m=1..4)}:
mersennes:= {seq(numtheory:-mersenne([i]), i=2..14)}:
R:= fermats union map(`-`,fermats,1) union mersennes union map(`+`,mersennes,1):
sort(convert(R union {1,9} minus {2,3,4,8},list)); # Robert Israel, Nov 25 2015

is(k) = isprimepower(k) || k==1;
for(k=1, 1e6, if(is(k) && is(k-1) + is(k+1) == 1, print1(k, ", "))) \\ Altug Alkan, Nov 23 2015

cp's OEIS Frontend

A264747 Prime powers n such that either n - 1 or n + 1 is a prime power, but not both.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI