A380976 a(0) = 0, a(1) = 1. Thereafter, a(n) = a(n-1) + a(n-2) converted to base n, read in base n+1.

0, 1, 1, 2, 3, 6, 10, 18, 31, 54, 93, 172, 300, 536, 955, 1686, 2976, 5224, 9491, 17089, 30618, 54774, 97553, 172749, 305164, 554749, 982005, 1757750, 3140769, 5584153, 9924579, 17582197, 31100841, 56191241, 99509416, 177595495, 316647651, 564436376, 1002970166

Offset: 0

Author

Kaleb Williams, Feb 10 2025

Keywords

• nonn
• base

Examples

			a(5) = a(4) + a(3) = 5 = 10_5 -> 10_6 = 6.
a(13) = a(12) + a(11) = 472 = 2A4_13 -> 2A4_14 = 536.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4302

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n, (l-> add(l[i]*
     (n+1)^(i-1), i=1..nops(l)))(convert(a(n-1)+a(n-2), base, n)))
    end:
seq(a(n), n=0..43);  # Alois P. Heinz, Feb 12 2025

Mathematica

A380976[n_] := A380976[n] = If[n <= 1, n, FromDigits[IntegerDigits[A380976[n-1] + A380976[n-2], n], n+1]];
Array[A380976, 50, 0] (* Paolo Xausa, Feb 14 2025 *)

Python

from itertools import count, islice
from sympy.ntheory.digits import digits
def fromdigits(digs, base): return sum(d*base**i for i, d in enumerate(digs[::-1]))
def agen(): # generator of terms
    yield from (a := [0, 1])
    for n in count(2):
        yield (an := fromdigits(digits(a[-2] + a[-1], n)[1:], n+1))
        a = [a[-1], an]
print(list(islice(agen(), 37))) # Michael S. Branicky, Feb 11 2025