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A054220
Concatenation of n in base 2 up to base 10 is divisible by at least one of these base b numbers, all numbers interpreted as decimals.
1
1, 2, 3, 4, 5, 8, 9, 10, 15, 16, 20, 22, 25, 38, 40, 44, 50, 55, 66, 68, 74, 75, 80, 95, 100, 110, 111, 125, 144, 175, 200, 230, 240, 250, 260, 265, 267, 268, 269, 300, 301, 316, 358, 375, 400, 440, 453, 476, 500, 514, 542, 620, 688, 875, 1000, 1096, 1120, 1250
OFFSET
1,2
EXAMPLE
n=9 -> 1001{2}=100{3}=21{4}=14{5}=13{6}=12{7}=11{8}=10{9}=9{10} -> 10011002114131211109 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))
return any(cn%int(sbi) == 0 for sbi in sb)
print([k for k in range(1, 1251) if ok(k)]) # Michael S. Branicky, Jan 25 2022
CROSSREFS
Cf. A054219.
Sequence in context: A217349 A329574 A087278 * A337801 A116214 A161389
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Feb 15 2000
EXTENSIONS
Data corrected by Sean A. Irvine, Jan 25 2022
STATUS
approved