A309737 Base conversion sequence: a(1) = 1; a(n) is the concatenation of all the previous terms, evaluated in base n-1, written in base n.

1, 1, 10, 213, 133130, 50044104412, 1456053604226211530303, 1355606752437672176235012441560305430335663, 211028537470000781652623227715306164580285678106041347266088244412145807188883237767

Offset

1,3

Comments

This will only work for n <= 10. To get a sequence that is defined for all n, it will be necessary to replace a(n) by a list of its "digits". So the result will be a triangle: 1 / 1 / 1,0 / 2,1,3 / ..., in which row n is a list of the digits written in base n. This should be an additional sequence with a cross-reference to this one. - N. J. A. Sloane, Sep 21 2019

See A349918 for the corresponding triangle. - Rémy Sigrist, Dec 05 2021

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10

Rémy Sigrist, PARI program for A309737

Formula

a(1) = 1; a(n) is the concatenation of all the previous terms, evaluated in base n-1, written in base n.

Example

For a(3) the previous terms are {1,1}. Evaluating the concatenation of those terms in base n-1 = 2 gives 11_2 = 3; converting that to base n = 3 gives 10_3, so a(3) = 10.
n=4: 1110_3 = 39_10 = 213_4, so a(4) = 213.

Prog

(PARI) See Links section.
(Python)
from sympy.ntheory.digits import digits
def fromdigits(d, b):
    n = 0
    for di in d: n *= b; n += di
    return n
def afull():
    alst, diglst = [1], [1]
    for n in range(2, 11):
        andigs = digits(fromdigits(diglst, n-1), n)[1:]
        alst.append(int("".join(map(str, andigs))))
        diglst.extend(andigs)
    return alst
print(afull()) # Michael S. Branicky, Dec 05 2021

Crossrefs

Cf. A349918.

Sequence in context: A332408 A245981 A245985 * A211912 A213788 A278125

Adjacent sequences: A309734 A309735 A309736 * A309738 A309739 A309740

Keyword

nonn,base,full,fini

Author

Moshe Levy, Aug 14 2019

Extensions

More terms from Rémy Sigrist, Dec 05 2021

Status

approved