A025674 - OEIS

A025674

Exponent of 8 (value of j) in n-th number of form 6^i*8^j.

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 7, 1, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 0, 7, 1, 8, 2, 9

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OFFSET

1,6

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences which agree for a long time but are different.

FORMULA

a(n) = A244413(A025627(n)/6^A025661(n)). - Amiram Eldar, Jul 09 2025

MATHEMATICA

With[{max = 10^12}, SortBy[Flatten[Table[{i, j}, {i, 0, Log[6, max]}, {j, 0, Log[8, max/6^i]}], 1], 6^#[[1]] * 8^#[[2]] &][[;; , 2]]] (* Amiram Eldar, Jul 09 2025 *)

PROG

(Python)

from sympy import integer_log, multiplicity

from oeis_sequences.OEISsequences import bisection

def A025674(n):

def f(x): return n+x-sum(integer_log(x>>3*i, 6)[0]+1 for i in range((x.bit_length()+2)//3))

return ((~(m:=bisection(f, n, n))&m-1).bit_length()-multiplicity(3, m))//3 # Chai Wah Wu, Aug 18 2026

CROSSREFS

Cf. A025627, A025661, A244413.

Differs from A025650 at a(1881).

Sequence in context: A025667 A025689 A025650 * A025681 A025659 A163351

Adjacent sequences: A025671 A025672 A025673 * A025675 A025676 A025677

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved