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A114137 Difference between first odd semiprime > 2^n and 2^n.

%I A114137 #6 Jun 14 2016 08:45:54
%S A114137 8,7,5,1,5,1,1,1,3,3,3,1,1,1,3,5,9,1,5,1,1,5,7,1,3,3,3,3,1,9,25,1,1,
%T A114137 11,7,3,7,15,19,3,1,5,3,1,31,3,7,21,3,9,7,11,3,11,3,29,9,29,25,9,45,1,
%U A114137 3,9,1
%N A114137 Difference between first odd semiprime > 2^n and 2^n.
%C A114137 A098147 is difference between first odd semiprime > 10^n and 10^n. In this powers of 2 sequence, does 1 occur infinitely often? Does every odd number occur?
%F A114137 a(n) = minimum integer k such that 2^n + k is an element of A046315. a(n) = minimum integer k such that A000079(n) + k is an element of A046315.
%e A114137 a(0) = 8 (the only even value here) because 2^0 + 8 = 9 = 3^2 is an odd semiprime.
%e A114137 a(1) = 7 because 2^1 + 7 = 9 = 3^2 is an odd semiprime.
%e A114137 a(2) = 5 because 2^2 + 5 = 9 = 3^2 is an odd semiprime.
%e A114137 a(3) = 1 because 2^3 + 1 = 9 = 3^2 is an odd semiprime.
%e A114137 a(4) = 5 because 2^4 + 5 = 21 = 3 * 7 is an odd semiprime.
%e A114137 a(5) = 1 because 2^5 + 1 = 33 = 3 * 11 is an odd semiprime.
%e A114137 a(6) = 1 because 2^6 + 1 = 65 = 5 * 13 is an odd semiprime.
%e A114137 a(10) = 3 because 2^10 + 3 = 1027 = 13 * 79 is an odd semiprime.
%e A114137 a(30) = 25 because 2^30 + 25 = 1073741849 = 29 * 37025581 is an odd semiprime.
%t A114137 a[n_] := Block[{z}, If[n == 0, z = 3, z = 2^n + 1]; While[ PrimeOmega[z] != 2, z += 2]; z - 2^n]; a /@ Range[0, 64] (* _Giovanni Resta_, Jun 14 2016 *)
%Y A114137 Cf. A001358, A098147.
%K A114137 easy,nonn
%O A114137 0,1
%A A114137 _Jonathan Vos Post_, Feb 03 2006
%E A114137 a(46) corrected by _Giovanni Resta_, Jun 14 2016