A230641 a(n) = n + (sum of digits in base-3 representation of n).

0, 2, 4, 4, 6, 8, 8, 10, 12, 10, 12, 14, 14, 16, 18, 18, 20, 22, 20, 22, 24, 24, 26, 28, 28, 30, 32, 28, 30, 32, 32, 34, 36, 36, 38, 40, 38, 40, 42, 42, 44, 46, 46, 48, 50, 48, 50, 52, 52, 54, 56, 56, 58, 60, 56, 58, 60, 60, 62, 64, 64, 66, 68, 66, 68, 70, 70, 72, 74, 74, 76, 78, 76, 78, 80, 80, 82, 84, 84, 86, 88, 82

Offset: 0

Author

N. J. A. Sloane, Oct 31 2013

Keywords

• nonn
• base

Comments

The image of this sequence is the set of nonnegative even numbers (A005843). Joshi (1973) proved that the sequence of base-q self numbers (analogous to A003052) is the sequence of odd numbers (A005408) for all odd q. - Amiram Eldar, Nov 28 2020

References

• V. S. Joshi, Ph.D. dissertation, Gujarat Univ., Ahmedabad (India), October, 1973.
• József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.

Links

• Donovan Johnson, Table of n, a(n) for n = 0..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Related base-3 sequences: A053735, A134451, A230641, A230642, A230643, A230853, A230854, A230855, A230856, A230639, A230640, A010063 (trajectory of 1)

Cf. A228088, A010061, A230091, A230092, A227915.

Programs

Haskell

a230641 n = a053735 n + n  -- Reinhard Zumkeller, May 19 2015

Mathematica

Table[n + Plus @@ IntegerDigits[n, 3], {n, 0, 100}] (* Amiram Eldar, Nov 28 2020 *)

Formula

a(n) = n + A053735(n). - Amiram Eldar, Nov 28 2020