A117416 Semiprime nearest to 3^n. In case of a tie, choose the smaller.

4, 4, 9, 26, 82, 247, 731, 2186, 6559, 19679, 59047, 177149, 531439, 1594322, 4782979, 14348905, 43046722, 129140159, 387420493, 1162261465, 3486784399, 10460353201, 31381059597, 94143178823, 282429536489, 847288609441

Offset

0,1

Comments

See also: A117405 Semiprime nearest to 2^n. A117387 Prime nearest to 2^n.

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = 3^n + A117416(n). a(n) = 3^n + Min{k such that A001358(i) + k = 3^n}.

Example

a(0) = 4 because 3^0 + 3 = 4 = A001358(1) and no semiprime is closer to 3^0.
a(1) = 4 because 3^1 + 1 = 4 = A001358(1) and no semiprime is closer to 3^1.
a(2) = 9 because 3^2 + 0 = 9 = 3^2 = A001358(3), no semiprime is closer to 3^2.
a(3) = 26 because 3^3 - 1 = 26 = 2 * 13, no semiprime is closer.
a(4) = 82 because 3^4 + 1 = 82 = 2 * 41, no semiprime is closer.
a(5) = 247 because 3^5 + 4 = 247 = 13 * 19, no semiprime is closer.

Mathematica

nsp[n_]:=Module[{c=3^n, a, b, j=1, k=1}, While[PrimeOmega[c-j]!=2, j++]; a=c-j; While[PrimeOmega[c+k]!=2, k++]; b=c+k; If[(b-c)<(c-a), b, a]]; Join[ {4, 4, 9}, Array[nsp, 30, 3]] (* Harvey P. Dale, Apr 11 2015 *)

Crossrefs

Cf. A000079, A001358, A117387, A117405, A117406, A117416.

Sequence in context: A118069 A089539 A324010 * A174943 A173317 A059811

Adjacent sequences: A117413 A117414 A117415 * A117417 A117418 A117419

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Mar 13 2006

Status

approved