A337732 Least positive number that has exactly n different representations as the sum of a number and the product of its decimal digits.

1, 0, 10, 50, 150, 1014, 9450, 8305, 283055, 931395, 92441055, 84305555, 28322235955

Offset: 0

Author

Bernard Schott, Sep 18 2020

Keywords

• nonn
• base
• more

Comments

Least integer m such that A230103(m) = n.

Examples

			10 = 5 + 5 = 10 + 1*0 and as 10 is the smallest number with 2 such representations, so, a(2) = 10.
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.
		

Crossrefs

Cf. A230099, A230103, A337718.

Cf. A337051 (similar for Bogotá numbers).

Programs

Mathematica

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 *)

PARI

f(n) = if (n==0, return(1)); sum(k=1, n, k+vecprod(digits(k)) == n); \\ A230103
a(n) = my(k=0); while(f(k) !=n, k++); k; \\ Michel Marcus, Sep 18 2020

Extensions

a(4)-a(7) from Michel Marcus, Sep 18 2020

a(8)-a(11) from Amiram Eldar, Sep 18 2020

a(12) from Bert Dobbelaere, Sep 22 2020