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Beyond repair - see A245628 for a better version.
1

%I #22 Jul 27 2014 13:39:01

%S 1,2,23,3,34,4,44,5,55,56,65,6,66,67,7,77,777,8,88,89,98,888,9,99,

%T 9999,13

%N Beyond repair - see A245628 for a better version.

%C Original definition was: "Rearrangement of natural numbers such that digit 'd' occurs exactly 'd' times. Once a cycle is completed, i.e., 9 occurs 9 times. The same is repeated. The first number of the second cycle would be a number containing 1 once and which has not occurred earlier."

%C Why is the first number of the second cycle 13 and not 10? 10 is the next number after 1 that contains 1 once. How is the first number of the second cycle chosen? Also, in the given example it is stated "a(26) = 13 as 12 has already occurred", but 12 does not occur in the terms prior to a(26). - _Felix Fröhlich_, Jul 26 2014

%C Comments from _Eric Angelini_, Jul 27 2014, in response to my asking him to investigate this sequence. (Start)

%C Murthy's seq is incoherent, for many reasons but two are sufficient:

%C <1> DEFINITION

%C "Rearrangement of natural numbers [...]"

%C ... No -- as "10" (or 100, 101, etc.) will never show up (because we would then not have zero "0"s)

%C <2> EXAMPLE

%C [...] "The second cycle starts at a(26) and a(26) = 13 as 12 has already occurred."

%C ... No, 12 has not occurred yet.

%C ... I propose the following definition and sequence ... (see A245628).

%C (End) - added by _N. J. A. Sloane_, Jul 27 2014

%Y See A245628 for a better version.

%K dead

%O 1,2

%A _Amarnath Murthy_, Jul 22 2005