A352333 a(1) = 1. For n >= 2, a(n) is the number whose base a(n-1) + 1 digit values, written in base 10, are the terms from a(1) through a(n-1).

1, 1, 3, 23, 14495, 44159351413734143, 167924255127116076603850942622864504418443431673483752235248022770009113621296308223

Offset

1,3

Comments

The minimal choice of a(n-1) + 1 for the base of the digit values of a(n) results in the slowest growing sequence in general. Can its growth rate be determined without computing further terms?

a(8) has 500 digits and a(9) has 3496 digits. - Michael S. Branicky, May 22 2022

Links

Table of n, a(n) for n=1..7.

Example

a(4) = 23 because in base a(3) + 1 = 3 + 1 = 4, the digit values 1, 1 and 3 represent 1*4^2 + 1*4^1 + 3*4^0 = 16 + 4 + 3 = 23.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    alst = [1]
    for n in count(2):
        yield alst[-1]
        b = alst[-1] + 1
        alst.append(sum(alst[-1-i]*b**i for i in range(len(alst))))
print(list(islice(agen(), 7))) # Michael S. Branicky, May 22 2022

Crossrefs

Sequence in context: A347680 A113577 A224700 * A355960 A264929 A204578

Adjacent sequences: A352330 A352331 A352332 * A352334 A352335 A352336

Keyword

nonn,base

Author

Tamas Sandor Nagy, May 22 2022

Status

approved