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

Author

Rémy Sigrist, Nov 27 2016

Keywords

• nonn
• base

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

Examples

			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.
		

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)

Crossrefs

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

Formula

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

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