A230865 a(n) = n + (sum of digits in base-5 representation of n).

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

Offset: 0

Author

N. J. A. Sloane, Nov 05 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

Crossrefs

Cf. A053824, A230641.

Programs

Mathematica

Table[n + Plus @@ IntegerDigits[n, 5], {n, 0, 100}] (* Amiram Eldar, Nov 28 2020 *)

Formula

a(n) = n + A053824(n). - Amiram Eldar, Nov 28 2020