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Numbers n such that one of 2^n-1 or 2^n+1 is semiprime, but not both.
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%I #22 Aug 23 2013 09:55:49

%S 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,

%T 92,97,103,104,109,127,128,131,137,139,148,149,191,197,227,241,256,

%U 269,271,281,293,313,356,373,379,421,457,487,523,596,692,701,727,809,881,971,983,997,1004,1061,1063

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

%e 2^3-1=7 is not a semiprime but 2^3+1 =9 is, so 3 is in the sequence.

%e 2^4-1 =15 is a semiprime but 2^4+1 =17 is not, so 4 is in the sequence.

%e 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.

%o (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

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

%K nonn,less

%O 1,1

%A _Irina Gerasimova_, May 28 2013

%E Original sequence of 4 small numbers replaced by a wider sequence. - _R. J. Mathar_, Jun 13 2013