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

Author

Alexandre Wajnberg & Eric Angelini, Sep 13 2004

Keywords

• base
• easy
• nice
• nonn

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

Crossrefs

Cf. A030655.

Programs

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 *)

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.