cp's OEIS Frontend

A316680 The integer 1358 and its infinite continuation (when iterating the rule explained in A316650 and in the Comment section here).

%I A316680 #16 Jul 15 2018 14:03:16
%S A316680 1358,7915,35917,143617,65281,29677,95710,435010,334624,152104,117004,
%T A316680 90004,69235,276910,1107610,6922510,27690010,110760010,692250010,
%U A316680 2769000010,11076000010,69225000010,276900000010,1107600000010,6922500000010,27690000000010,110760000000010,692250000000010,2769000000000010
%N A316680 The integer 1358 and its infinite continuation (when iterating the rule explained in A316650 and in the Comment section here).
%C A316680 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).
%e A316680 1358/17 gives 79 with remainder 15;
%e A316680 7915/22 gives 359 with remainder 17;
%e A316680 35917/25 gives 1436 with remainder 17;
%e A316680 143617/22 gives 6528 remainder 1;
%e A316680 ...
%e A316680 After 6922510 starts a devilish inflation "from the middle", in a ternary cycle:
%e A316680 6922510
%e A316680 27690010
%e A316680 110760010
%e A316680 692250010
%e A316680 2769000010
%e A316680 11076000010
%e A316680 69225000010
%e A316680 276900000010
%e A316680 1107600000010
%e A316680 6922500000010
%e A316680 27690000000010
%e A316680 110760000000010
%e A316680 692250000000010
%e A316680 2769000000000010
%e A316680 11076000000000010
%e A316680 69225000000000010
%e A316680 276900000000000010
%e A316680 1107600000000000010
%e A316680 6922500000000000010
%e A316680 ...
%e A316680 We have:
%e A316680 2769(k zeros)10
%e A316680 11076(k zeros)10
%e A316680 69225(k zeros)10
%e A316680 then:
%e A316680 2769(k+2 zeros)10
%e A316680 11076(k+2 zeros)10
%e A316680 69225(k+2 zeros)10
%e A316680 then:
%e A316680 2769(k+4 zeros)10
%e A316680 11076(k+4 zeros)10
%e A316680 69225(k+4 zeros)10
%e A316680 Etc.
%t A316680 NestList[FromDigits@ Flatten[IntegerDigits@ # & /@ QuotientRemainder[#, Total[IntegerDigits@ #]]] &, 1358, 28] (* _Michael De Vlieger_, Jul 10 2018 *)
%Y A316680 Cf. A316650 (where the rule is explained).
%Y A316680 Cf. A316679 (for an equivalent pattern produced by 907).
%K A316680 base,nonn
%O A316680 1,1
%A A316680 _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 10 2018