A061987 - OEIS

A061987

Number of times n-th distinct value is repeated in sequence b(k) = 1 + b(floor(k/2)) + b(floor(k/3)) with b(0) = 0, i.e., in A061984; also number of times n-th distinct row is repeated in square array T(n,k) = T(n-1,k) + T(n-1,floor(k/2)) + T(n-1,floor(k/3)) with T(0,0) = 1, i.e., in A061980.

1, 1, 1, 1, 2, 2, 1, 3, 4, 2, 6, 3, 5, 4, 12, 6, 10, 8, 9, 15, 12, 20, 16, 18, 30, 24, 27, 13, 32, 36, 60, 48, 54, 26, 64, 72, 81, 39, 96, 108, 52, 128, 144, 162, 78, 192, 216, 104, 139, 117, 288, 324, 156, 384, 432, 208, 278, 234, 576, 648, 312, 417, 351, 864, 416, 556

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

For n > 0: a(n) = A003586(n+1) - A003586(n) and a(A084791(n)) = A084788(n).

Also number of times A160519(n+1) is repeated in A088468. - Reinhard Zumkeller, May 16 2009

In the 14th century Levi Ben Gerson proved that a(n) > 1 for all n > 6; see A003586, A235365, A235366, A236210. - Jonathan Sondow, Jan 20 2014

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..100 from Reinhard Zumkeller)

Eric Weisstein's World of Mathematics, Smooth Number

FORMULA

a(n) = A061986(A061985(n)).

PROG

(Haskell)

import Data.List (group)

a061987 n = a061987_list !! n

a061987_list = map length $ group a061984_list

-- Reinhard Zumkeller, Jan 11 2014

(Python)

from sympy import integer_log

from oeis_sequences.OEISsequences import bisection

def A061987(n):

def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1))

return -(m:=bisection(f, n, n))+bisection(lambda x:f(x)+1, m, m) if n else 1 # Chai Wah Wu, Mar 09 2026

CROSSREFS

Sequence in context: A103923 A349432 A186711 * A323899 A182630 A208805

Adjacent sequences: A061984 A061985 A061986 * A061988 A061989 A061990

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 24 2001

EXTENSIONS

More terms from Reinhard Zumkeller, Jun 03 2003

STATUS

approved