A062845 When expressed in base 2 and then interpreted in base 3, is a multiple of the original number.

0, 1, 5, 6, 10, 12, 30, 36, 60, 120, 180, 215, 216, 252, 360, 430, 432, 1080, 2730, 3276, 13710, 14724, 16380, 20520, 24624, 24840, 27125, 27420, 32760, 38880, 48606, 49091, 54250, 54840, 97212, 98280

Offset: 1

Author

Erich Friedman, Jul 21 2001

Keywords

• base
• nonn

Comments

The numbers 2*m, 4*m and 8*m are also terms of the sequence for m=a(122). - Dimiter Skordev, Mar 29 2020

Examples

			30 = 11110_2; 11110_3 = 120 = 4*30.
		

Links

• Dimiter Skordev, Table of n, a(n) for n = 1..122 (terms < 10^15, terms 1..36 from Erich Friedman, 37..111 from Dimiter Skordev, 112..120 from Giovanni Resta)
• Dimiter Skordev, Pascal program
• Dimiter Skordev, Python script

Crossrefs

Cf. A062846, A062847, A062848, A062849, A062850, A032533, A062853.

Cf. A005836.

Programs

Magma

[0] cat [k:k in [1..100000]|Seqint(Intseq(Seqint(Intseq(k, 2))),3) mod k eq 0]; // Marius A. Burtea, Dec 29 2019

Mathematica

{0} ~Join~ Select[Range[10^5], Mod[ FromDigits[ IntegerDigits[#, 2], 3], #] == 0 &] (* Giovanni Resta, Dec 10 2019 *)

PARI

isok(m) = (m==0) || fromdigits(digits(m, 2), 3) % m == 0; \\ Michel Marcus, Feb 15 2020

Python

def BaseUp(n,b):
    up, b1 = 0, 1
    while n > 0:
        up, b1, n = up+(n%b)*b1, b1*(b+1), n//b
    return up
n, k = 1, 0
print(1,0)
while n < 35:
    n, k = n+1, k+1
    while BaseUp(k,2)%k != 0:
        k = k+1
    print(n,k) # A.H.M. Smeets, Mar 31 2020