A068994 -id:A068994 - cp's OEIS frontend

A096549 Least exponent k such that the lowest n digits in the decimal representation of 2^k are even.

1, 6, 10, 11, 19, 43, 50, 50, 71, 71, 523, 590, 590, 12106, 12106, 12106, 12106, 56590, 505206, 1570511, 1570511, 4033966, 4033966, 9525771, 24045606, 24045606, 57862019, 183002599, 183002599, 877875719, 877875719, 877875719, 3789535319

Offset: 1

Hugo Pfoertner, Jul 07 2004

This problem was discussed in a thread "Power of 2 with all even digits?" in the newsgroup sci.math (Jun 25 2004) with contributions from Edwin Clark, James Waldby, Bertram Felgenhauer, Richard Tobin, Oskar Lanzi III and others.

a(47) > 15258789062500. - Robert Xiao, Mar 23 2025

			a(5)=19 because 2^19=524288 is the smallest power of 2 that has a decimal representation ending in 5 even digits.

Robert Xiao, Table of n, a(n) for n = 1..46
Newsgroup sci.math, Power of 2 with all even digits?

Cf. A000079, A068994.

a(21)-a(33) from Richard Tobin (richard(AT)cogsci.ed.ac.uk), Jun 29 2004

A272697 Powers of 2 with exactly one odd decimal digit.

Original entry on oeis.org

1, 16, 32, 128, 256, 1024, 4096, 262144, 524288, 8388608

Offset: 1

Seiichi Manyama, May 04 2016

Inspired by A068994 (Powers of 2 such that number of odd digits is 0).
No additional terms up to 2^10000.
No additional terms < 2^500000. - Chai Wah Wu, May 22 2016
No additional terms < 2^(10^10). - Michael S. Branicky, Apr 16 2023

Cf. A068994, A272698.

Select[2^Range[0, 50000], Total@ Pick[DigitCount@ #, {1, 0, 1, 0, 1, 0, 1, 0, 1, 0}, 1] == 1 &] (* Michael De Vlieger, May 04 2016 *)
od1Q[n_]:=Count[IntegerDigits[n],?(OddQ[#]&)]==1; Select[2^Range[0,100],od1Q] (* _Harvey P. Dale, Sep 04 2024 *)

ary = [1]
s = 1
(1..10 ** 4).each{|i|
  s *= 2
  j = s.to_s.split('').map(&:to_i).select{|i| i % 2 == 1}.size
  ary << s if j == 1
}
p ary

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A096549 Least exponent k such that the lowest n digits in the decimal representation of 2^k are even.

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A272697 Powers of 2 with exactly one odd decimal digit.

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