A278743 For a base n>1: consider the lexicographically least strictly increasing sequence c_n such that, for any m>0, Sum_{k=1..m} c_n(k) can be computed without carries in base n; the sequence c_n is (conjecturally) eventually linear, and a(n) gives its order.

1, 3, 2, 5, 9, 3, 7, 4, 17, 4, 9, 15, 21, 11, 5, 11, 25, 25, 13, 7, 6, 13, 7, 29, 15, 16, 25, 7, 15, 9, 33, 17, 10, 28, 57, 8, 17, 49, 37, 19, 10, 31, 63, 21, 9, 19, 43, 41, 21, 34, 34, 69, 23, 12, 10, 21, 13, 45, 23, 51, 37, 75, 25, 13, 67, 11, 23, 42, 49, 25

Offset

2,2

Comments

More precisely, we conjecture that, for any n>1, there are two constants k0 and b such that c_n(k + a(n)) = c_n(k)*n^b for any k>k0. [Corrected by Rémy Sigrist, Dec 24 2016]

For the values of k0 and b see A280051 and A280052. - N. J. A. Sloane, Jan 06 2017

Links

Rémy Sigrist, Table of n, a(n) for n = 2..10000

Rémy Sigrist, PERL program for A278743

Rémy Sigrist, Illustration of the initial terms

Rémy Sigrist, Plot of A278743 vs A280051

N. J. A. Sloane, Table of n, a(n), k0(n), b(n) for n=2..42 (A précis of Sigrist's "Illustration" file)

Formula

a(A000124(n)) = n for any n>0.

a(A000124(n)+1) = 2*n + 1 for any n>0.

Example

c_2 = A000079, and A000079 has order 1, hence a(2)=1.
c_10 = A278742, and A278742 has order 17, hence a(10)=17.
See also Links section.

Crossrefs

Cf. A000079, A000124, A278742, A279732, A280051, A280052.

Sequence in context: A049922 A160106 A243786 * A081974 A257883 A169755

Adjacent sequences: A278740 A278741 A278742 * A278744 A278745 A278746

Keyword

nonn,base

Author

Rémy Sigrist, Nov 27 2016

Status

approved