A117405 - OEIS

%I #10 Jun 15 2016 10:38:35

%S 4,4,4,9,15,33,65,129,254,511,1027,2047,4097,8193,16382,32765,65531,

%T 131073,262142,524289,1048577,2097149,4194311,8388607,16777219,

%U 33554429,67108867,134217731,268435457,536870918,1073741821,2147483649,4294967297,8589934589

%N Semiprime nearest to 2^n. (In case of a tie, choose the smaller).

%C Semiprime analog of A117387 Prime nearest to 2^n. (In case of a tie, choose the smaller). After n=2, never again is a(n) a power of 2.

%F a(n) = 2^n + A117406(n).

%e a(0) = 4 because 2^0 + 3 = 4 = A001358(1) and no semiprime is closer to 2^0.

%e a(1) = 4 because 2^1 + 2 = 4 = A001358(1) and no semiprime is closer to 2^1.

%e a(2) = 4 because 2^2 + 0 = 4 = A001358(1) and no semiprime is closer to 2^2.

%e a(3) = 9 because 2^3 + 1 = 9 = 3^2 = A001358(3), no semiprime is closer to 2^3.

%e a(4) = 15 because 2^4 - 1 = 15 = 3 * 5 and no semiprime is closer.

%e a(5) = 33 because 2^5 + 1 = 33 = 3 * 11 and no semiprime is closer to 2^5.

%e a(6) = 65 because 2^6 + 1 = 65 = 5 * 13 and no semiprime is closer to 2^6.

%e a(7) = 129 because 2^7 + 1 = 129 = 3 * 43 and no semiprime is closer to 2^7.

%e a(8) = 254 because 2^8 - 2 = 254 = 2 * 127 and no semiprime is closer to 2^8.

%t a[n_] := Catch@Block[{p = 2^n, k = 0}, While[True, If[p > k && PrimeOmega[p - k] == 2, Throw[p - k]]; If[PrimeOmega[p + k] == 2, Throw[p + k]]; k++]]; a /@ Range[20] (* _Giovanni Resta_, Jun 15 2016 *)

%Y Cf. A000079, A001358, A117387, A117406.

%K easy,nonn,less

%O 0,1

%A _Jonathan Vos Post_, Mar 13 2006

%E Corrected and extended by _Giovanni Resta_, Jun 15 2016