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
Examples
Rd(1639) = 1639*639*39*9 = 367609671, Ld(1639) = 1639*163*16*1 = 4274512 and 367609671 == 1639 (mod 4274512).
Programs
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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]));
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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 *)
Comments