A038364 Numbers n such that n = (product of digits of n) + (sum of digits of n).

0, 19, 29, 39, 49, 59, 69, 79, 89, 99

Offset

1,2

Comments

A number n with m digits belongs to the sequence if K1*K2*K3*...*Km-9_(m-1)*K1-9_(m-2)*K2....=0 where Ki are the digits of n and 9_(m-1) is a repdigit with 9 repeated (m-1) times. Hence m=2, so sequence is complete.

Links

Table of n, a(n) for n=1..10.

Maple

select(proc(t) local d; d:= convert(t, base, 10); convert(d, `+`)+convert(d, `*`)=t end proc, [$0..100]); # Robert Israel, Dec 16 2014

Mathematica

Select[Range[100], # == Times @@ IntegerDigits[#] + Plus @@ IntegerDigits[#] &] (* Michael De Vlieger, Dec 26 2014 *)

Prog

(PARI) isok(n) = my(d=digits(n)); n == (sum(i=1, #d, d[i]) + prod(i=1, #d, d[i])); \\ Michel Marcus, Apr 06 2014

Crossrefs

Sequence in context: A061763 A088474 A087097 * A151360 A329106 A109276

Adjacent sequences: A038361 A038362 A038363 * A038365 A038366 A038367

Keyword

fini,nonn,base,full

Author

Felice Russo

Status

approved