A098080 Nontrivial slowest increasing sequence whose succession of digits is that of the nonnegative integers.

0, 12, 34, 56, 78, 910, 1112, 1314, 1516, 1718, 1920, 2122, 2324, 2526, 2728, 2930, 3132, 3334, 3536, 3738, 3940, 4142, 4344, 4546, 4748, 4950, 5152, 5354, 5556, 5758, 5960, 6162, 6364, 6566, 6768, 6970, 7172, 7374, 7576, 7778, 7980, 8182, 8384, 8586, 8788, 8990, 9192, 9394, 9596, 9798, 99100, 101102

Offset

0,2

Comments

Beginning with 1, 23, 45, etc. gives a similar sequence which however grows more quickly. Other sequences can be generated by varying the "template" of the succession of digits (such as the decimal expansion of Pi, e, and so on).

1, 23, 45, 67, 89, 101, 112, 131, 415, 1617, 1819, 2021, 2223, ..., 9899, 10010, 110210, 310410, 510610, 710810, 911011, 1112113, ... does grow faster, but what about 1, 23, 45, 67, 89, 101, 112, 131, 415, 1617, ..., (2k)(2k+1), ...? The claim of "slowest" requires that after a(1), the smallest possible option must always be used (9899->10010 instead of 9899->100101). - Danny Rorabaugh, Nov 27 2015

Links

Table of n, a(n) for n=0..51.

Formula

Write down the sequence of nonnegative integers and consider its succession of digits. Divide up into chunks of minimal length (and not beginning with 0) so that chunks are increasing numbers in order to form the slowest ever increasing sequence of slices (disregarding the number of digits) of the succession of the digits of the whole numbers.

Mathematica

jd[{a_, b_}]:=Module[{ida=IntegerDigits[a], idb=IntegerDigits[b]}, FromDigits[ Join[ida, idb]]]; Join[{0}, jd/@Partition[Range[110], 2]] (* Harvey P. Dale, Feb 20 2012 *)

Crossrefs

Cf. A030655.

Sequence in context: A228595 A077295 A030655 * A068517 A113748 A069125

Adjacent sequences: A098077 A098078 A098079 * A098081 A098082 A098083

Keyword

base,easy,nice,nonn

Author

Alexandre Wajnberg & Eric Angelini, Sep 13 2004

Status

approved