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 A316679 The integer 907 and its infinite growing pattern (when iterating the rule explained in A316650 and hereunder, in the Comment section). 2
 907, 5611, 4318, 26914, 12238, 76414, 34738, 138913, 555613, 2222413, 13890013, 55560013, 222240013, 1389000013, 5556000013, 22224000013, 138900000013, 555600000013, 2222400000013, 13890000000013, 55560000000013, 222240000000013, 1389000000000013, 5556000000000013, 22224000000000013 (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 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). LINKS Table of n, a(n) for n=1..25. 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 Cf. A316650 (where the rule is explained) and A316680 (for the number 1358 that generates a similar pattern). Sequence in context: A031939 A253228 A134075 * A177998 A253347 A253354 Adjacent sequences: A316676 A316677 A316678 * A316680 A316681 A316682 KEYWORD base,nonn AUTHOR Eric Angelini and Jean-Marc Falcoz, Jul 10 2018 STATUS approved

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Last modified June 14 04:01 EDT 2024. Contains 373393 sequences. (Running on oeis4.)