A292931 -id:A292931 - cp's OEIS frontend

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

M. F. Hasler, Sep 27 2017

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.

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

Cf. A004166, A292931.

[n lt 2 select 0 else &+Intseq(3^n)/9: n in [0..100]]; // Vincenzo Librandi, Sep 28 2017

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

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

PARI
```
a(n)=sumdigits(3^n)\9
```

from _future_ import division
def A292995(n):
    return sum(int(d) for d in str(3**n))//9 # Chai Wah Wu, Sep 28 2017

cp's OEIS Frontend

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

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