A324321 Numbers k such that Rd(k) == k (mod Ld(k)), where Rd(k) = A067079 and Ld(k) = A067080.

21, 23, 25, 27, 29, 31, 34, 37, 41, 45, 49, 51, 56, 61, 67, 71, 78, 81, 89, 91, 101, 109, 114, 118, 145, 175, 201, 209, 251, 267, 301, 365, 401, 501, 529, 601, 701, 801, 901, 1001, 1639, 2001, 3001, 4001, 5001, 6001, 7001, 8001, 9001, 10001, 20001, 30001, 40001

Offset

1,1

Comments

All numbers of the form d*10^k+1, where d = 1,2,3,4,5,6,7,8,9 and k>0, are part of the sequence except 11.

Links

Table of n, a(n) for n=1..53.

Example

Rd(1639) = 1639*639*39*9 = 367609671, Ld(1639) = 1639*163*16*1 = 4274512 and 367609671 == 1639 (mod 4274512).

Maple

op(select(n->n=mul(n mod 10^k, k=1..ilog10(n)+1) mod mul(trunc(n/10^k), k=0..ilog10(n)), [$1..40001]));

Mathematica

Select[Range[10^5], Mod[Times @@ Map[FromDigits, NestWhileList[Rest@ # &, IntegerDigits@ #, Length@ # > 1 &]], Times @@ Map[FromDigits, NestWhileList[Most@ # &, IntegerDigits@ #, Length@ # > 1 &]]] == # &] (* Michael De Vlieger, Feb 25 2019 *)

Crossrefs

Cf. A067079, A067080, A324322.

Sequence in context: A104669 A156891 A095459 * A095455 A095451 A169887

Adjacent sequences: A324318 A324319 A324320 * A324322 A324323 A324324

Keyword

nonn,easy

Author

Paolo P. Lava, Feb 22 2019

Status

approved