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

Author

Felice Russo

Keywords

• fini
• nonn
• base
• full

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.

Programs

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 *)

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