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%I #13 Nov 18 2020 21:32:55
%S 0,1,3,6,10,65,1211,8988,16171616,1015101610151015,
%T 11101115111011161110111511101115,
%U 1212121112121216121212111212121712121211121212161212121112121216
%N a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.
%C 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.
%e a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
%e a(6) = {6+6, 5+6} = 1211.
%p a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
%p seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
%p end:
%p seq(a(n), n=0..12); # _Alois P. Heinz_, Nov 15 2020
%t Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* _Michael De Vlieger_, Nov 13 2020 *)
%Y Cf. A061511-A061750, A061581-A061587, A089718, A337770.
%K nonn,base
%O 0,3
%A _Jamie Robert Creasey_, Nov 07 2020
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