A117405 Semiprime nearest to 2^n. (In case of a tie, choose the smaller).

4, 4, 4, 9, 15, 33, 65, 129, 254, 511, 1027, 2047, 4097, 8193, 16382, 32765, 65531, 131073, 262142, 524289, 1048577, 2097149, 4194311, 8388607, 16777219, 33554429, 67108867, 134217731, 268435457, 536870918, 1073741821, 2147483649, 4294967297, 8589934589

Offset: 0

Author

Jonathan Vos Post, Mar 13 2006

Keywords

• easy
• nonn
• less

Comments

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.

Examples

			a(0) = 4 because 2^0 + 3 = 4 = A001358(1) and no semiprime is closer to 2^0.
a(1) = 4 because 2^1 + 2 = 4 = A001358(1) and no semiprime is closer to 2^1.
a(2) = 4 because 2^2 + 0 = 4 = A001358(1) and no semiprime is closer to 2^2.
a(3) = 9 because 2^3 + 1 = 9 = 3^2 = A001358(3), no semiprime is closer to 2^3.
a(4) = 15 because 2^4 - 1 = 15 = 3 * 5 and no semiprime is closer.
a(5) = 33 because 2^5 + 1 = 33 = 3 * 11 and no semiprime is closer to 2^5.
a(6) = 65 because 2^6 + 1 = 65 = 5 * 13 and no semiprime is closer to 2^6.
a(7) = 129 because 2^7 + 1 = 129 = 3 * 43 and no semiprime is closer to 2^7.
a(8) = 254 because 2^8 - 2 = 254 = 2 * 127 and no semiprime is closer to 2^8.
		

Crossrefs

Cf. A000079, A001358, A117387, A117406.

Programs

Mathematica

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 *)

Formula

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

Extensions

Corrected and extended by Giovanni Resta, Jun 15 2016