A243021 Numbers n such that n appears in the sequence beginning with the digit-sum of n and extended by adding successive digit-sums.

12, 15, 18, 21, 24, 27, 30, 32, 33, 36, 37, 39, 45, 47, 51, 52, 54, 57, 58, 59, 62, 63, 69, 72, 81, 84, 90, 96, 99, 101, 103, 107, 109, 111, 114, 115, 117, 119, 120, 123, 126, 129, 135, 141, 144, 147, 153, 159, 161, 162, 163, 169, 171, 173, 174, 180, 184, 185, 186, 189, 197, 199, 201, 204, 207, 210, 213, 216, 219, 221, 225, 226, 231, 234, 236, 237

Offset

1,1

Comments

Numbers n>9 with following property: form a sequence b(i) whose initial term is digit-sum(n). Later terms are given by the rule that b(i) = b(i-1) + digit-sum(b(i-1)) and n itself appears in the sequence.

Links

Table of n, a(n) for n=1..76.

Formula

b(i) = b(i-1) + digit-sum(b(i-1))

Example

When n = 0..9, the sequence immediately produces n. The sequence for 12 is seeded with digital-sum(12) = 3, 3 + 3 = 6, 6 + 6 = 12. 15 yields 6, 6 + 6 = 12, 12 + 3 = 15. 18 yields 9, 9 + 9 = 18. 21 yields 3, 3 + 3 = 6, 6 + 6 = 12, 12 + 3 = 15, 15 + 6 = 21.

Crossrefs

Cf. A007629, A243140.

Sequence in context: A281880 A153047 A265128 * A164782 A207830 A348788

Adjacent sequences: A243018 A243019 A243020 * A243022 A243023 A243024

Keyword

nonn,base,easy

Author

Anthony Sand, May 29 2014

Extensions

Added comments based on those for A007629.

Status

approved