login
A332876
a(n) is the smallest positive multiple of n whose decimal expansion includes a digit (other than a trailing zero) whose removal yields a proper multiple of n.
0
12, 14, 36, 28, 105, 102, 147, 136, 108, 120, 242, 204, 286, 238, 330, 352, 374, 306, 2109, 140, 462, 484, 2047, 408, 150, 572, 594, 756, 3219, 360, 682, 864, 2937, 1326, 770, 792, 4107, 2128, 4329, 280, 3649, 1638, 3827, 1232, 990, 2530, 5217, 1344, 5439, 1050
OFFSET
1,1
COMMENTS
This sequence is a variant of A309631; but here, when we strike out the right digit, it is forbidden that the obtained number is equal to n.
About the origin of this sequence, see comments in A309631.
The first quotients a(n)/n are 12, 7, 12, 7, 21 ,17, 21, 17, 12, 12, 22, 17, 22, 17, 22, ...
REFERENCES
Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, Ivan Yashchenko, Moscow Mathematical Olympiads, 2000-2005,Problem 3, Level D, 2004, MSRI, 2011, p. 21 and 130/131
EXAMPLE
a(7) = 147 because 147 = 7*21 and if we strike out "7", 14 is also divisible by 7, and there is no integer < 147 with that property.
MATHEMATICA
del[n_] := Block[{m = 10^IntegerExponent[n, 10], d}, d = IntegerDigits[n/m]; Table[ FromDigits[Delete[d, k]] m, {k, Length@ d}]]; a[n_] := Block[{k = n, v}, While[! AnyTrue[del[k], # > n && Mod[#, n] == 0 &], k += n]; k]; Array[a, 50] (* Giovanni Resta, Feb 28 2020 *)
CROSSREFS
Cf. A309631 (original version), A328567 (binary variant).
Sequence in context: A140810 A330197 A127401 * A256786 A337874 A337876
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Feb 28 2020
EXTENSIONS
More terms from Giovanni Resta, Feb 28 2020
Name improved by Rémy Sigrist and Jon E. Schoenfield, Feb 28 2020
STATUS
approved