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

Author

Bernard Schott, Feb 28 2020

Keywords

• nonn
• base

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, ...

Examples

			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.
		

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

• Index to sequences related to Olympiads.

Crossrefs

Cf. A309631 (original version), A328567 (binary variant).

Programs

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 *)

Extensions

More terms from Giovanni Resta, Feb 28 2020

Name improved by Rémy Sigrist and Jon E. Schoenfield, Feb 28 2020