A230641 -id:A230641 - cp's OEIS frontend

A230856 Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly four solutions.

248, 492, 978, 1222, 1708, 1952, 2192, 2196, 2436, 2680, 3166, 3410, 3896, 4140, 4380, 4384, 4624, 4868, 5354, 5598, 6084, 6328, 6566, 6572, 6810, 7054, 7540, 7784, 8270, 8514, 8754, 8758, 8998, 9242, 9728, 9972, 10458, 10702, 10942, 10946, 11186, 11430, 11916, 12160, 12646, 12890, 13128

Offset: 1

N. J. A. Sloane, Oct 31 2013

Donovan Johnson, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

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

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

Original entry on oeis.org

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

N. J. A. Sloane, Nov 05 2013

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

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.

Donovan Johnson, Table of n, a(n) for n = 0..10000

Cf. A053824, A230641.

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

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

A350229 a(n) is the sum of n and the balanced ternary digits in n.

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, Jan 09 2022

The image of this sequence is the set of nonnegative even numbers (A005843).

			For n = 42:
- the balanced ternary representation of 42 is "1TTT0",
- so a(42) = 42 + 1 - 1 - 1 - 1 + 0 = 40.

See A062028, A092391, A230641 for similar sequences.

Cf. A005843, A065363, A174658 (fixed points).

Array[# + Total[If[First@ # == 0, Rest@ #, #] &[Prepend[IntegerDigits[#, 3], 0] //. {x___, y_, k_ /; k > 1, z___} :> {x, y + 1, k - 3, z}]] &, 70, 0] (* Michael De Vlieger, Jan 15 2022 *)

a(n) = my (v=n, d); while (n, n=(n-d=[0,1,-1][1+n%3])/3; v+=d); v

a(n) = n + A065363(n).

a(n) = n iff n belongs to A174658.

cp's OEIS Frontend

A230856 Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly four solutions.

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

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A350229 a(n) is the sum of n and the balanced ternary digits in n.

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