1,3

Starting at a(2), this is column 2 of Table 1 of the Donald M. Davis paper, p.32; the other columns show that the sequence is nearly understood in a deeper sense. The numbers e_p(k,n) defined as min{nu_p(S(k,j)j!): j >= n} appear frequently in algebraic topology. Here S(k,j) is the Stirling number of the second kind, and nu_p(-) the exponent of p. The author and Sun proved that if L is sufficiently large, then e_p((p-1)p^L + n -1, n) >= n-1+nu_p([n/p]!). In this paper, we determine the set of integers n for which equality holds in this inequality when p=2 and 3. The condition is roughly that, in the base-p expansion of n, the sum of two consecutive digits must always be less than p. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 17 2008

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

L. Babai, On the length of subgroup chains in the symmetric group, Commun. Algebra, 14 (1986), 1729-1736.

Peter J. Cameron; Ron Solomon; Alexandre Turull, Chains of subgroups in symmetric groups, J. Algebra 127 (1989), no. 2, 340-352.

T. D. Noe, Table of n, a(n) for n=1..1000

J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II

Donald M. Davis, Divisibility by 2 and 3 of certain Stirling numbers, Jul 16, 2008.

ceiling(3n/2) - b(n) - 1, where b(n) = # 1's in binary expansion of n (A000120).

G.f.: 1/(1-x) * (-1/(1-x^2) + Sum(k>=0, x^2^k/(1-x^2^k))). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 13 2002

a(n) = ceiling(3n/2) - b(n) - 1, where b(n) = # 1's in binary expansion of n (A000120). - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 17 2008

A000120 := proc(n) local w, m, i: w := 0: m := n: while m > 0 do i := m mod 2: w := w+i: m := (m-i)/2: od: w: end: for n from 1 to 100 do printf(`%d, `, ceil(3*n/2) - A000120(n) - 1) od:

Adjacent sequences: A007235 A007236 A007237 this_sequence A007239 A007240 A007241

Sequence in context: A126424 A138620 A098166 this_sequence A083875 A080762 A047570

nonn,nice

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 19 2001