A334681 Lexicographically earliest sequence of distinct positive integers such that the digital root of the cumulative sum so far divides a(n).

1, 9, 10, 8, 12, 6, 16, 2, 18, 27, 28, 14, 3, 36, 40, 5, 42, 4, 17, 45, 46, 20, 15, 48, 21, 22, 24, 11, 54, 63, 64, 26, 72, 81, 82, 30, 23, 84, 33, 85, 32, 88, 29, 90, 99, 100, 35, 105, 25, 41, 108, 117, 118, 44, 120, 34, 53, 126, 130, 50, 135, 136, 56, 51, 144, 153, 154, 62, 156, 52, 71, 160, 38, 162, 168, 39

Offset

1,2

Links

Carole Dubois, Table of n, a(n) for n = 1..5001

Example

The sequence starts hereunder with the S line (this sequence); then comes the Q line (cumulative sum of S' terms); then comes the R line (digital root of Q at this point):
S = 1,  9, 10,  8, 12,  6, 16,  2, 18,  27,  28,  14,   3,  36,  40,...
Q = 1, 10, 20, 28, 40, 46, 62, 64, 82, 109, 137, 151, 154, 190, 230,...
R = 1,  1,  2,  1,  4,  1,  8,  1,  1,   1,   2,   7,   1,   1,   5,...
We see that the term R divides the term S on top of the 3-level column.

Crossrefs

Cf. A010888 (digital root of n).

Sequence in context: A205151 A167691 A107434 * A020508 A158001 A157763

Adjacent sequences: A334678 A334679 A334680 * A334682 A334683 A334684

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, May 08 2020

Status

approved