A226116 Numbers n such that one of 2^n-1 or 2^n+1 is semiprime, but not both.

3, 4, 5, 6, 7, 9, 12, 13, 17, 19, 20, 28, 31, 32, 37, 40, 41, 43, 49, 59, 61, 64, 67, 79, 83, 92, 97, 103, 104, 109, 127, 128, 131, 137, 139, 148, 149, 191, 197, 227, 241, 256, 269, 271, 281, 293, 313, 356, 373, 379, 421, 457, 487, 523, 596, 692, 701, 727, 809, 881, 971, 983, 997, 1004, 1061, 1063

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Example

2^3-1=7 is not a semiprime but 2^3+1 =9 is, so 3 is in the sequence.
2^4-1 =15 is a semiprime but 2^4+1 =17 is not, so 4 is in the sequence.
2^8-1 =255 is a 3-prime (not a 2-prime) and 2^8+1 =257 is a prime (not a 2-prime), so 8 is not in the sequence.

Prog

(PARI) isok(n) = {nbm = bigomega(2^n-1); nbp = bigomega(2^n+1); return (((nbm == 2) || (nbp == 2)) && ! ((nbm == 2) && (nbp == 2))); } \\ Michel Marcus, Aug 23 2013

Crossrefs

Cf. A001358, A046051, A054992, A092558, A092559.

Sequence in context: A096515 A100586 A139372 * A128659 A364083 A022555

Adjacent sequences: A226113 A226114 A226115 * A226117 A226118 A226119

Keyword

nonn,less

Author

Irina Gerasimova, May 28 2013

Extensions

Original sequence of 4 small numbers replaced by a wider sequence. - R. J. Mathar, Jun 13 2013

Status

approved