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A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n. 0
0, 1, 3, 6, 10, 65, 1211, 8988, 16171616, 1015101610151015, 11101115111011161110111511101115, 1212121112121216121212111212121712121211121212161212121112121216 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A352057 A343811 A071299 * A351131 A061380 A350993
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)