A114137 - OEIS

%I #6 Jun 14 2016 08:45:54

%S 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 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 3,9,1

%N Difference between first odd semiprime > 2^n and 2^n.

%C 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 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 a(0) = 8 (the only even value here) because 2^0 + 8 = 9 = 3^2 is an odd semiprime.

%e a(1) = 7 because 2^1 + 7 = 9 = 3^2 is an odd semiprime.

%e a(2) = 5 because 2^2 + 5 = 9 = 3^2 is an odd semiprime.

%e a(3) = 1 because 2^3 + 1 = 9 = 3^2 is an odd semiprime.

%e a(4) = 5 because 2^4 + 5 = 21 = 3 * 7 is an odd semiprime.

%e a(5) = 1 because 2^5 + 1 = 33 = 3 * 11 is an odd semiprime.

%e a(6) = 1 because 2^6 + 1 = 65 = 5 * 13 is an odd semiprime.

%e a(10) = 3 because 2^10 + 3 = 1027 = 13 * 79 is an odd semiprime.

%e a(30) = 25 because 2^30 + 25 = 1073741849 = 29 * 37025581 is an odd semiprime.

%t 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 Cf. A001358, A098147.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Feb 03 2006

%E a(46) corrected by _Giovanni Resta_, Jun 14 2016