A118872 Numbers k such that digit sum of 3^k is a power of 3.

0, 1, 2, 3, 4, 5, 9, 10, 11, 13, 16, 17, 21, 27, 31, 35, 36, 39, 114, 119, 973, 1005, 1010, 1025, 3006, 3029, 3040, 9128, 9215, 9227, 9316, 27431, 27442, 27515, 27519, 27554, 82632, 82746, 82763, 82784, 83111, 246838, 247206, 247388, 247406, 247447, 741310, 742154

Offset: 1

Author

Zak Seidov, May 24 2006

Keywords

• base
• nonn

Comments

a(47) > 677750. - Ray Chandler, Jun 16 2006

a(47) <= 741310. If a(47) < 741310 then a(47) < 720000. a(48) <= 742154. If a(48) < 741310 then a(48) < 720000. - David A. Corneth, Nov 23 2022

Examples

			3^39 = 4052555153018976267 with digit sum 81 = 3^4, so 39 is a term.
		

Crossrefs

Cf. A004166 (sum of digits of 3^n).

Programs

Mathematica

Do[If[IntegerQ[Log[3, Plus @@ IntegerDigits[3^n]]], Print[n]], {n, 0, 677750}];

PARI

is(n) = my(s = sumdigits(3^n)); s == 3^logint(s, 3) \\ David A. Corneth, Nov 23 2022

Formula

A067500(n) = 3^a(n).

Extensions

Extended by Ray Chandler, Jun 16 2006

a(47) and a(48) from Jon E. Schoenfield, Nov 25 2022