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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.
7
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Nov 27 2016
STATUS
approved