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%I #31 Sep 23 2020 02:59:02
%S 1,0,10,50,150,1014,9450,8305,283055,931395,92441055,84305555,
%T 28322235955
%N Least positive number that has exactly n different representations as the sum of a number and the product of its decimal digits.
%C Least integer m such that A230103(m) = n.
%e 10 = 5 + 5 = 10 + 1*0 and as 10 is the smallest number with 2 such representations, so, a(2) = 10.
%e 50 = 35 + 3*5 = 42 * 4*2 = 50 + 5*0 and as 50 is the smallest number with 3 such representations, so, a(3) = 50.
%t f[n_] := n + Times @@ IntegerDigits[n]; m = 10^6; v = Table[0, {m}]; Do[i = f[n] + 1; If[i <= m, v[[i]]++], {n, 0, m}]; s = {1}; k = 1; While[(p = Position[v, k]) != {}, AppendTo[s, p[[1, 1]] - 1]; k++]; s (* _Amiram Eldar_, Sep 18 2020 *)
%o (PARI) f(n) = if (n==0, return(1)); sum(k=1, n, k+vecprod(digits(k)) == n); \\ A230103
%o a(n) = my(k=0); while(f(k) !=n, k++); k; \\ _Michel Marcus_, Sep 18 2020
%Y Cf. A230099, A230103, A337718.
%Y Cf. A337051 (similar for Bogotá numbers).
%K nonn,base,more
%O 0,3
%A _Bernard Schott_, Sep 18 2020
%E a(4)-a(7) from _Michel Marcus_, Sep 18 2020
%E a(8)-a(11) from _Amiram Eldar_, Sep 18 2020
%E a(12) from _Bert Dobbelaere_, Sep 22 2020
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