OFFSET
1,1
COMMENTS
It is conjectured, when iterating the idea explained in A316650 ("Result when n is divided by the sum of its digits and the resulting integer is concatenated to the remainder"), that all integers will end either on a fixed point (the first ones are listed in A052224) or grow forever (like 907 or 1358).
EXAMPLE
907/16 gives 56 with remainder 11;
5611/13 gives 431 with remainder 8;
4318/16 gives 269 with remainder 14;
26914/22 gives 122 with remainder 38;
. . .
Now from 2222413 on, starts a devilish 0-inflation "from the middle" in a ternary cycle:
2222413
13890013
55560013
222240013
1389000013
5556000013
22224000013
138900000013
555600000013
2222400000013
13890000000013
55560000000013
222240000000013
1389000000000013
5556000000000013
22224000000000013
138900000000000013
555600000000000013
2222400000000000013
. . .
We have:
1389(k zeros)13
5556(k zeros)13
22224(k zeros)13
then:
1389(k+2 zeros)13
5556(k+2 zeros)13
22224(k+2 zeros)13
then:
1389(k+4 zeros)13
5556(k+4 zeros)13
22224(k+4 zeros)13
Etc.
MATHEMATICA
NestList[FromDigits@ Flatten[IntegerDigits@ # & /@ QuotientRemainder[#, Total[IntegerDigits@ #]]] &, 907, 24] (* Michael De Vlieger, Jul 10 2018 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jul 10 2018
STATUS
approved