A191475 - OEIS

A191475

Values of i in the numbers 2^i*3^j, i >= 1, j >= 1 (A033845).

1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 9, 6, 3, 8, 5, 2, 10, 7, 4, 1, 9, 6, 3, 11, 8, 5, 2, 10, 7, 4, 12, 1, 9, 6, 3, 11, 8, 5, 13, 2, 10, 7, 4, 12, 1, 9, 6, 14, 3, 11, 8, 5, 13, 2, 10, 7, 15, 4, 12, 1, 9, 6, 14, 3, 11

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OFFSET

1,2

COMMENTS

Signature sequence of log_2(3) (A020857). - R. J. Mathar, May 27 2024

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

Index entries for sequences related to signature sequences

EXAMPLE

a(10) = 2 because A033845(10) = 108 = 2^2*3^3.

a(100) = 2 because A033845(100) = 59872 = 2^8*3^7.

a(1000) = 56 because A033845(1000) = 216172782113783808 = 2^56*3^1.

MATHEMATICA

mx = 1000000; t = Select[Sort[Flatten[Table[2^i 3^j, {i, Log[2, mx]}, {j, Log[3, mx]}]]], # <= mx &]; Table[FactorInteger[i][[1, 2]], {i, t}] (* T. D. Noe, Aug 31 2012 *)

PROG

(Python)

from sympy import integer_log

def A191475(n):

def bisection(f, kmin=0, kmax=1):

while f(kmax) > kmax: kmax <<= 1

while kmax-kmin > 1:

kmid = kmax+kmin>>1

if f(kmid) <= kmid:

kmax = kmid

else:

kmin = kmid

return kmax

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

return 1+(~(m:=bisection(f, n, n))&m-1).bit_length() # Chai Wah Wu, Sep 15 2024

CROSSREFS

Cf. A003586 (numbers 2^i*3^j, i >= 0, j >= 0), A033845 (numbers 2^i*3^j, i >= 1, j >= 1), A191476 (values of j), A020857.

Sequence in context: A058933 A087470 A373215 * A158456 A084531 A023129

Adjacent sequences: A191472 A191473 A191474 * A191476 A191477 A191478

KEYWORD

nonn

AUTHOR

Zak Seidov, Aug 30 2012

EXTENSIONS

Edited by N. J. A. Sloane, May 26 2024

STATUS

approved