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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.

%I A332876 #38 Oct 01 2020 20:33:37
%S A332876 12,14,36,28,105,102,147,136,108,120,242,204,286,238,330,352,374,306,
%T A332876 2109,140,462,484,2047,408,150,572,594,756,3219,360,682,864,2937,1326,
%U A332876 770,792,4107,2128,4329,280,3649,1638,3827,1232,990,2530,5217,1344,5439,1050
%N 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.
%C A332876 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.
%C A332876 About the origin of this sequence, see comments in A309631.
%C A332876 The first quotients a(n)/n are 12, 7, 12, 7, 21 ,17, 21, 17, 12, 12, 22, 17, 22, 17, 22, ...
%D A332876 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
%H A332876 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e A332876 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.
%t A332876 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 *)
%Y A332876 Cf. A309631 (original version), A328567 (binary variant).
%K A332876 nonn,base
%O A332876 1,1
%A A332876 _Bernard Schott_, Feb 28 2020
%E A332876 More terms from _Giovanni Resta_, Feb 28 2020
%E A332876 Name improved by _Rémy Sigrist_ and _Jon E. Schoenfield_, Feb 28 2020