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