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

Author

Jamie Robert Creasey, Nov 07 2020

Keywords

• nonn
• base

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.

Examples

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

Crossrefs

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

Programs

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 *)