A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.

0, 1, 3, 6, 10, 65, 1211, 8988, 16171616, 1015101610151015, 11101115111011161110111511101115, 1212121112121216121212111212121712121211121212161212121112121216

Offset

0,3

Comments

This sequence is the additive counterpart of the digit factorials which, unlike the digit factorials, increases at a faster pace. A061511 and its relatives bear similarities to this sequence, but each of these increase at varying rates depending on the chosen constant. However, unlike these sequences, the constant increases by 1 each time. If digits within a(n-1) exceed 9 when one adds a constant, we ignore carrying and replace the digit with its correct value, thus 9+1 = 10. a(15) has 1024 digits.

Links

Table of n, a(n) for n=0..11.

Example

a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
a(6) = {6+6, 5+6} = 1211.

Maple

a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
      seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 15 2020

Mathematica

Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* Michael De Vlieger, Nov 13 2020 *)

Crossrefs

Cf. A061511-A061750, A061581-A061587, A089718, A337770.

Sequence in context: A352057 A343811 A071299 * A351131 A061380 A350993

Adjacent sequences: A338764 A338765 A338766 * A338768 A338769 A338770

Keyword

nonn,base

Author

Jamie Robert Creasey, Nov 07 2020

Status

approved