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

0,1

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.

Links

Table of n, a(n) for n=0..33.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000079, A001358, A117387, A117406.

Sequence in context: A211547 A075561 A256796 * A013601 A219802 A219460

Adjacent sequences: A117402 A117403 A117404 * A117406 A117407 A117408

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Mar 13 2006

Extensions

Corrected and extended by Giovanni Resta, Jun 15 2016

Status

approved