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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

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OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..48.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A333050 A328119 A118732 * A046029 A303600 A194410

Adjacent sequences: A118869 A118870 A118871 * A118873 A118874 A118875

KEYWORD

base,nonn

AUTHOR

Zak Seidov, May 24 2006

EXTENSIONS

Extended by Ray Chandler, Jun 16 2006

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

STATUS

approved