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.

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

Links

Table of n, a(n) for n=1..50.

Index to sequences related to Olympiads.

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

Adjacent sequences: A332873 A332874 A332875 * A332877 A332878 A332879

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