A066282 Numbers k such that k = (product of nonzero digits of k) * (sum of digits of k).

0, 1, 135, 144, 1088

Offset

1,3

Comments

No further term below 5*10^7. The sequence can be shown to be finite by a slight modification of D. Wilson's proof of the finiteness of A038369.

Links

Table of n, a(n) for n=1..5.

René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)

Example

(1+0+8+8) * (1*8*8) = 17*64 = 1088, so 1088 belongs to the sequence.

Mathematica

Do[ d = Sort[ IntegerDigits[n]]; While[ First[d] == 0, d = Drop[d, 1]]; If[n == Apply[ Plus, d] Apply[ Times, d], Print[n]], {n, 0, 5*10^7} ]

Prog

(ARIBAS) function a066282(a, b: integer); var n, k, j, p, d: integer; s: string; begin for n := a to b do s := itoa(n); k := 0; p := 1; for j := 0 to length(s) - 1 do d := atoi(s[j..j]); k := k + d; if d > 0 then p := p*d; end; end; if n = p*k then write(n, ", "); end; end; end; a066282(0, 25000).
(PARI) a066282(a, b) = local(n, k, q, p, d); for(n=a, b, k=0; p=1; q=n; while(q>0, d=divrem(q, 10); q=d[1]; k=k+d[2]; p=p*max(1, d[2])); if(n==p*k, print1(n, ", ")))
a066282(0, 25000)

Crossrefs

Fixed points of A062331.

Cf. A023651, A038364, A038369, A062237.

Sequence in context: A335950 A355002 A038369 * A235809 A066176 A025363

Adjacent sequences: A066279 A066280 A066281 * A066283 A066284 A066285

Keyword

base,nonn,more

Author

Klaus Brockhaus, Dec 13 2001

Extensions

Offset corrected by Mohammed Yaseen, Jul 21 2022

Status

approved