A292995 Sum of digits of 3^n (A004166) divided by 9.

0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 2, 3, 5, 4, 3, 3, 5, 4, 5, 3, 5, 6, 6, 7, 7, 9, 8, 8, 7, 9, 7, 8, 11, 9, 9, 10, 10, 9, 10, 11, 10, 12, 10, 11, 12, 14, 13, 12, 16, 13, 13, 15, 12, 10, 10, 12, 14, 13, 11, 15, 17, 17, 16, 15, 13, 18, 17, 17, 16, 20, 18, 17, 19, 20, 17, 18

Offset

0,7

Comments

All terms A004166(n), n >= 2, are multiples of 9.

For the first two terms, the (zero) integer part of the fractional values (1/9 and 3/9) is taken: This seems to be the most natural extension of the maybe more natural variant of this sequence which would start only at offset n = 2.

Divisibility of A004166(n) by any prime different from 3 is equivalent to divisibility of a(n) by that prime. For example, indices of terms of A004166 divisible by 7, listed in A292931, are also exactly the indices > 1 of terms a(n) divisible by 7.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Maple

0, 0, seq(convert(convert(3^n, base, 10), `+`)/9, n=2..100); # Robert Israel, Sep 28 2017

Mathematica

Rest[Table[Sum[DigitCount[(3^n)][[i]] i, {i, 9}] / 9, {n, 100}]] (* Vincenzo Librandi, Sep 28 2017 *)

Prog

(PARI) a(n)=sumdigits(3^n)\9
(Magma) [n lt 2 select 0 else &+Intseq(3^n)/9: n in [0..100]]; // Vincenzo Librandi, Sep 28 2017
(Python)
from __future__ import division
def A292995(n):
    return sum(int(d) for d in str(3**n))//9 # Chai Wah Wu, Sep 28 2017

Crossrefs

Cf. A004166, A292931.

Sequence in context: A080967 A078570 A295284 * A037179 A127971 A319290

Adjacent sequences: A292992 A292993 A292994 * A292996 A292997 A292998

Keyword

nonn,base

Author

M. F. Hasler, Sep 27 2017

Status

approved