A065448 Numbers k such that k is congruent to the product of its digits modulo the sum of its digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 20, 29, 30, 31, 33, 36, 39, 40, 49, 50, 52, 55, 59, 60, 63, 64, 69, 70, 71, 77, 79, 80, 89, 90, 99, 100, 102, 108, 110, 113, 118, 119, 120, 132, 140, 150, 166, 168, 180, 190, 195, 198, 200, 201, 204

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

14 is in the sequence because 14 == 4 (mod 5).

Mathematica

Select[Range[2000], Mod[ # - Apply[Times, IntegerDigits[[ # ]]], Apply[Plus, IntegerDigits[[ # ]]]] == 0 &]

Prog

(PARI) SumD(x)= { local(s=0); while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } ProdD(x)= { local(p=1); while (x>9 && p>0, p*=(x-10*(x\10)); x\=10); return(p*x) } { n=0; for (m=1, 10^9, p=ProdD(m); s=SumD(m); if ((m - p)%s == 0, write("b065448.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 19 2009

Crossrefs

Cf. A007953, A007954.

Sequence in context: A034894 A263564 A061430 * A254656 A211408 A107322

Adjacent sequences: A065445 A065446 A065447 * A065449 A065450 A065451

Keyword

base,nonn

Author

Santi Spadaro, Nov 18 2001

Status

approved