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 with 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
1358/17 gives 79 with remainder 15;
7915/22 gives 359 with remainder 17;
35917/25 gives 1436 with remainder 17;
143617/22 gives 6528 remainder 1;
...
After 6922510 starts a devilish inflation "from the middle", in a ternary cycle:
6922510
27690010
110760010
692250010
2769000010
11076000010
69225000010
276900000010
1107600000010
6922500000010
27690000000010
110760000000010
692250000000010
2769000000000010
11076000000000010
69225000000000010
276900000000000010
1107600000000000010
6922500000000000010
...
We have:
2769(k zeros)10
11076(k zeros)10
69225(k zeros)10
then:
2769(k+2 zeros)10
11076(k+2 zeros)10
69225(k+2 zeros)10
then:
2769(k+4 zeros)10
11076(k+4 zeros)10
69225(k+4 zeros)10
Etc.
MATHEMATICA
NestList[FromDigits@ Flatten[IntegerDigits@ # & /@ QuotientRemainder[#, Total[IntegerDigits@ #]]] &, 1358, 28] (* Michael De Vlieger, Jul 10 2018 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jul 10 2018
STATUS
approved