A340138 a(1)=0, a(n+1) = the least m not already in the sequence such that the decimal digital root r of a(n-1) is found somewhere among the decimal digits of m.

0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 21, 23, 25, 27, 29, 20, 22, 24, 26, 28, 31, 34, 37, 41, 35, 38, 32, 45, 39, 30, 33, 36, 49, 40, 42, 46, 51, 56, 52, 47, 62, 48, 43, 57, 53, 58, 44, 68, 50, 54, 59, 55, 61, 67, 64, 71, 78, 60

Offset: 1

Author

Michael De Vlieger, Jan 21 2021

Keywords

• nonn
• base

Comments

a(n) = 10^k occurs before n = 10^k for 0 < k <= 5.

Conjecture: permutation of the nonnegative numbers.

A decimal version of A339607, a permutation of the integers having to do with binary weight, but instead using digital root rather than digit sum. The plots of these sequences have similar features.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Plot (n, a(n)) for 1 <= n <= 10^3 with records in dark red and least unused numbers in dark blue, with records of a(n)-n in red, many labeled, and records of n-a(n) in blue, many labeled.
• Michael De Vlieger, Logarithmic plot (n, a(n)-n) for 1 <= n <= 10^5 with records labeled in red, records of n-a(n) labeled in blue, and zeros plotted in black.

Crossrefs

Cf. A248025, A338191, A339607.

Programs

Mathematica

Block[{a = {0, 10}, k, r}, Do[k = 1; r = # + 9 Boole[# == 0] &@ Mod[a[[-1]], 9]; While[Nand[FreeQ[a, k], ! FreeQ[IntegerDigits[k], r]], k++]; AppendTo[a, k], 66]; a]