cp's OEIS Frontend

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.

%I A278743 #39 Jan 07 2017 14:40:45
%S A278743 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,
%T A278743 15,9,33,17,10,28,57,8,17,49,37,19,10,31,63,21,9,19,43,41,21,34,34,69,
%U A278743 23,12,10,21,13,45,23,51,37,75,25,13,67,11,23,42,49,25
%N 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.
%C A278743 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]
%C A278743 For the values of k0 and b see A280051 and A280052. - _N. J. A. Sloane_, Jan 06 2017
%H A278743 Rémy Sigrist, <a href="/A278743/b278743.txt">Table of n, a(n) for n = 2..10000</a>
%H A278743 Rémy Sigrist, <a href="/A278743/a278743.pl.txt">PERL program for A278743</a>
%H A278743 Rémy Sigrist, <a href="/A278743/a278743.pdf">Illustration of the initial terms</a>
%H A278743 Rémy Sigrist, <a href="/A280051/a280051.png">Plot of A278743 vs A280051</a>
%H A278743 N. J. A. Sloane, <a href="/A278743/a278743.txt">Table of n, a(n), k0(n), b(n) for n=2..42</a> (A précis of Sigrist's "Illustration" file)
%F A278743 a(A000124(n)) = n for any n>0.
%F A278743 a(A000124(n)+1) = 2*n + 1 for any n>0.
%e A278743 c_2 = A000079, and A000079 has order 1, hence a(2)=1.
%e A278743 c_10 = A278742, and A278742 has order 17, hence a(10)=17.
%e A278743 See also Links section.
%Y A278743 Cf. A000079, A000124, A278742, A279732, A280051, A280052.
%K A278743 nonn,base
%O A278743 2,2
%A A278743 _Rémy Sigrist_, Nov 27 2016