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A167154 Numbers where terms in A167153 change parity: a(n)+1 is in A167153, but a(n)-1 is not. 0

%I #10 Jun 09 2016 22:03:37

%S 9,30,49,70,89,200,399,600,799,1000

%N Numbers where terms in A167153 change parity: a(n)+1 is in A167153, but a(n)-1 is not.

%C Sequence A167153 consists of runs of numbers of the same parity. It is conjectured that each time the parity changes, there is a gap of 3 numbers, and the sequence goes on with the successor a(n)+1 (of opposite parity) of the first "missing" term a(n) in the run of terms of given parity (a(n-1)+1, a(n-1)+3, ..., a(n)-2).

%H E. Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Digitsum.htm">a(n) is the digitsum of a(a(n))</a>, November 2009.

%H E. Angelini, <a href="/A167152/a167152.pdf">a(n) is the digitsum of a(a(n))</a> [Cached copy, with permission]

%e Sequence A167153 starts 10,12,14,... so a(1)=9 is the predecessor of the first even term 10 = a(1)+1 in the sequence.

%e Then the sequence changes parity at ...,26, 28, 31, 33,..., i.e. a(2)-2 = 28 is the last term in this run of even numbers, a(2) = 30 is missing, and the sequence goes on with odd numbers starting at a(2)+1 = 31.

%e That run of odd numbers ends with a(3)-2 = 47; a(3) = 49 is missing, and the sequence goes on with even numbers starting at a(3)+1 = 50.

%Y Cf. A167152. A167153.

%K more,nonn,base

%O 1,1

%A _Eric Angelini_ and _M. F. Hasler_, Nov 03 2009

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Last modified July 15 01:36 EDT 2024. Contains 374323 sequences. (Running on oeis4.)