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A117405 Semiprime nearest to 2^n. (In case of a tie, choose the smaller). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 13 14:58 EST 2017. Contains 295958 sequences.