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A316680 The integer 1358 and its infinite continuation (when iterating the rule explained in A316650 and in the Comment section here). 2
1358, 7915, 35917, 143617, 65281, 29677, 95710, 435010, 334624, 152104, 117004, 90004, 69235, 276910, 1107610, 6922510, 27690010, 110760010, 692250010, 2769000010, 11076000010, 69225000010, 276900000010, 1107600000010, 6922500000010, 27690000000010, 110760000000010, 692250000000010, 2769000000000010 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Table of n, a(n) for n=1..29.

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

Cf. A316650 (where the rule is explained).

Cf. A316679 (for an equivalent pattern produced by 907).

Sequence in context: A172379 A192319 A125270 * A252379 A175696 A023091

Adjacent sequences:  A316677 A316678 A316679 * A316681 A316682 A316683

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Jul 10 2018

STATUS

approved

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Last modified August 11 19:26 EDT 2022. Contains 356066 sequences. (Running on oeis4.)