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A244859
Least positive multiple of n which when written in base 10 is either a repunit or of the form 1111....0000.
3
0, 1, 10, 111, 100, 10, 1110, 111111, 1000, 111111111, 10, 11, 11100, 111111, 1111110, 1110, 10000, 1111111111111111, 1111111110, 111111111111111111, 100, 111111, 110, 1111111111111111111111, 111000, 100, 1111110, 111111111111111111111111111, 11111100
OFFSET
0,3
COMMENTS
a(1017) has 1008 digits. - Michael S. Branicky, Feb 22 2024
LINKS
Michael S. Branicky, Table of n, a(n) for n = 0..1016 (terms 101..936 from Robert Israel, terms 0..100 from Chai Wah Wu).
Chai Wah Wu, Pigeonholes and repunits, Amer. Math. Monthly, 121 (2014), 529-533.
MAPLE
A244859:= proc(n) local m, d2, d5;
d2:= padic:-ordp(n, 2);
d5:= padic:-ordp(n, 5);
m:= n/2^d2/5^d5;
10^max(d2, d5)*(10^numtheory:-order(10, 9*m)-1)/9
end proc:
A244859(0):= 0:
seq(A244859(n), n= 0..100); # Robert Israel, Jul 08 2014
PROG
(Python)
def a(n):
if n == 0: return 0
moddict = {0: 0}
for e in range(1, n+2):
repe = (10**e-1)//9
r = repe%n
if r in moddict:
return repe - moddict[r]
else:
moddict[r] = repe
print([a(n) for n in range(29)]) # Michael S. Branicky, Feb 22 2024
CROSSREFS
Equal to A004290 for the first 7 terms.
Sequence in context: A228006 A004290 A257344 * A159551 A105991 A284352
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Jul 07 2014
STATUS
approved