|
|
A337732
|
|
Least positive number that has exactly n different representations as the sum of a number and the product of its decimal digits.
|
|
1
|
|
|
1, 0, 10, 50, 150, 1014, 9450, 8305, 283055, 931395, 92441055, 84305555, 28322235955
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Least integer m such that A230103(m) = n.
|
|
LINKS
|
|
|
EXAMPLE
|
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.
|
|
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 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
Cf. A337051 (similar for Bogotá numbers).
|
|
KEYWORD
|
nonn,base,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|