A346383 Numbers that leave their digital root as the remainder when the product of their digits is divided by the sum of their digits.

37, 38, 39, 73, 83, 93, 99, 146, 164, 247, 274, 299, 339, 348, 368, 384, 386, 393, 416, 427, 438, 449, 461, 472, 483, 494, 614, 638, 641, 679, 683, 697, 699, 724, 742, 769, 796, 834, 836, 843, 863, 929, 933, 944, 967, 969, 976, 992, 996, 1149, 1156, 1165, 1179

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

3*7 == 1 (mod 3+7), digital root of 37 is 1, so 37 is a term.

Maple

filter:= proc(n) local L; L:= convert(n, base, 10); convert(L, `*`) mod convert(L, `+`) = [9, $1..8][(n mod 9)+1] end proc;

Mathematica

l={}; Do[If[Mod[Times@@IntegerDigits@n, Total[IntegerDigits[n]]]==FixedPoint[Total[IntegerDigits[#, 10]] &, n], AppendTo[l, n]], {n, 0, 1000}]; l

Prog

(PARI) isok(m) = my(d=digits(m)); (vecprod(d) % vecsum(d)) == ((m-1)%9 + 1); \\ Michel Marcus, Jul 15 2021

Crossrefs

Cf. A007953, A007954, A010888.

Sequence in context: A185698 A043611 A296871 * A337453 A071887 A168143

Adjacent sequences: A346380 A346381 A346382 * A346384 A346385 A346386

Keyword

nonn,base

Author

Metin Sariyar, Jul 14 2021

Status

approved