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

1,3

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

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Cf. A005836.

Sequence in context: A105953 A164095 A102506 * A236307 A166563 A005847

Adjacent sequences: A062842 A062843 A062844 * A062846 A062847 A062848

Keyword

base,nonn

Author

Erich Friedman, Jul 21 2001

Status

approved