

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



