cp's OEIS Frontend

A117406 Integer k such that 2^n + k = A117405(n).

%I A117406 #10 Jun 15 2016 10:38:27
%S A117406 3,2,0,1,-1,1,1,1,-2,-1,3,-1,1,1,-2,-3,-5,1,-2,1,1,-3,7,-1,3,-3,3,3,1,
%T A117406 6,-3,1,1,-3,-3,-3,-3,-1,18,3,1,-1,3,1,-3,3,7,-9,3,-1,7,-5,3,11,-3,-5,
%U A117406 6,-9,-3,-1,-3,1,-2,9,1,5,3,-1,-5,-13,9,-3,-7,-3
%N A117406 Integer k such that 2^n + k = A117405(n).
%C A117406 After n=2, never again is a(n) = 0. Semiprime analog of A117388 Integer k such that 2^n + k = A117387(n). A117387(n) is prime nearest to 2^n. (In case of a tie, choose the smaller).
%F A117406 a(n) = A117405(n) - 2^n. a(n) = Min{k such that A001358(i) + k = 2^j}.
%e A117406 a(0) = 3 because 2^0 + 3 = 4 = A001358(1) and no semiprime is closer to 2^0.
%e A117406 a(1) = 2 because 2^1 + 2 = 4 = A001358(1) and no semiprime is closer to 2^1.
%e A117406 a(2) = 0 because 2^2 + 0 = 4 = A001358(1) and no semiprime is closer to 2^2.
%e A117406 a(3) = 1 because 2^3 + 1 = 9 = 3^2 = A001358(3), no semiprime is closer to 2^3.
%e A117406 a(4) = -1 because 2^4 - 1 = 15 = 3 * 5 and no semiprime is closer.
%e A117406 a(5) = 1 because 2^5 + 1 = 33 = 3 * 11 and no semiprime is closer to 2^5.
%e A117406 a(6) = 1 because 2^6 + 1 = 65 = 5 * 13 and no semiprime is closer to 2^6.
%e A117406 a(7) = 1 because 2^7 + 1 = 129 = 3 * 43 and no semiprime is closer to 2^7.
%e A117406 a(8) = -2 because 2^8 - 2 = 254 = 2 * 127 and no semiprime is closer to 2^8.
%t A117406 a[n_] := Catch@Block[{p = 2^n, k = 0}, While[True, If[p > k && PrimeOmega[p - k] == 2, Throw[-k]]; If[PrimeOmega[p + k] == 2, Throw[k]]; k++]]; a /@ Range[0, 80] a /@ Range[0, 80] (* _Giovanni Resta_, Jun 15 2016 *)
%Y A117406 Cf. A000079, A001358, A117387, A117405.
%K A117406 easy,sign,less
%O A117406 0,1
%A A117406 _Jonathan Vos Post_, Mar 13 2006
%E A117406 Corrected and extended by _Giovanni Resta_, Jun 15 2016