A054219 Concatenation of n in base 10 down to base 2 is divisible by at least one of these base b numbers, all numbers interpreted as decimals.

1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 20, 24, 32, 36, 40, 64, 70, 72, 80, 96, 100, 104, 116, 128, 131, 144, 160, 168, 192, 200, 216, 256, 288, 292, 293, 300, 320, 336, 344, 360, 362, 370, 380, 400, 432, 512, 536, 544, 560, 576, 640, 648, 727, 768, 800, 864

Offset

1,2

Links

Table of n, a(n) for n=1..58.

Example

n=9 -> 9{10}=10{9}=11{8}=12{7}=13{6}=14{5}=21{4}=100{3}=1001{2} -> 91011121314211001001 which is divisible by 21 (from 9 in base 4).

Prog

(Python)
from sympy.ntheory.digits import digits
def ok(n):
    sb = ["".join(str(d) for d in digits(n, b)[1:]) for b in range(2, 11)]
    cn = int("".join(sb[::-1]))
    return any(cn%int(sbi) == 0 for sbi in sb)
print([k for k in range(1, 865) if ok(k)]) # Michael S. Branicky, Jan 25 2022

Crossrefs

Cf. A054220.

Sequence in context: A256389 A225729 A035033 * A196277 A368385 A280196

Adjacent sequences: A054216 A054217 A054218 * A054220 A054221 A054222

Keyword

nonn,base

Author

Patrick De Geest, Feb 15 2000

Extensions

Data corrected by Sean A. Irvine, Jan 25 2022

Status

approved