A227019 Numbers n such that exactly one of {2^n-1, 2^n+1, 2^n+3} is semiprime.

3, 4, 6, 7, 8, 10, 12, 13, 14, 17, 19, 20, 24, 25, 26, 27, 28, 31, 35, 37, 39, 41, 42, 43, 45, 48, 49, 52, 54, 59, 62, 66, 67, 76, 79, 83, 87, 92, 97, 99, 100, 103, 104, 109, 114, 115, 127, 131, 132, 137, 139, 142, 148, 149, 151, 158, 162, 172, 189, 190, 191, 197, 207, 210, 220, 226, 227, 241, 255, 256, 269, 271, 281, 289, 291, 293, 294, 295

Offset

1,1

Comments

Roughly analogous to A226116 (numbers n such that one of 2^n-1 or 2^n+1 is semiprime, but not both); but for one out of 3 in the set rather than 1 out of 2.

Links

Table of n, a(n) for n=1..78.

Example

6 is in the sequence because 2^6 - 1 = 63 = 3^2 * 7 has three prime factors (with multiplicity), 2^6 + 1 = 65 = 5 * 13 is semiprime, and 2^6 + 3 = 67 is prime.

Mathematica

smQ[n_]:=Count[2^n+{1, 3, -1}, _?(PrimeOmega[#]==2&)]==1; Select[Range[ 300], smQ] (* Harvey P. Dale, Jan 30 2014 *)

Prog

(PARI) issemi(n)=bigomega(n)==2
is(n)=my(N=2^n); if(issemi(N-1), !issemi(N+1)&&!issemi(N+3), issemi(N+1)+issemi(N+3)==1) \\ Charles R Greathouse IV, Jun 28 2013

Crossrefs

Cf. A001358, A226116.

Sequence in context: A007378 A274829 A087758 * A105454 A364006 A283482

Adjacent sequences: A227016 A227017 A227018 * A227020 A227021 A227022

Keyword

nonn

Author

Jonathan Vos Post, Jun 27 2013

Extensions

a(7)-a(61) from Charles R Greathouse IV, Jun 28 2013

a(62)-a(78) from Charles R Greathouse IV, Jul 03 2013

Status

approved