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

Author

Jonathan Vos Post, Mar 13 2006

Keywords

• easy
• nonn
• less

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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 *)

Formula

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