A100035 - OEIS

A100035

a(n+1) occurs not earlier as a neighbor of terms = a(n): either it is the greatest number < a(n) or, if no such number exists, the smallest number > a(n); a(1) = 1.

1, 2, 3, 1, 4, 3, 5, 4, 2, 5, 1, 6, 5, 7, 6, 4, 7, 3, 6, 2, 7, 1, 8, 7, 9, 8, 6, 9, 5, 8, 4, 9, 3, 8, 2, 9, 1, 10, 9, 11, 10, 8, 11, 7, 10, 6, 11, 5, 10, 4, 11, 3, 10, 2, 11, 1, 12, 11, 13, 12, 10, 13, 9, 12, 8, 13, 7, 12, 6, 13, 5, 12, 4, 13, 3, 12, 2, 13, 1, 14, 13, 15, 14, 12, 15, 11, 14, 10

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OFFSET

1,2

COMMENTS

The natural numbers (A000027) occur infinitely many times as disjoint subsequences, see the example below and A100036, A100037, A100038 and A100039: exactly one k exists for all x < y such that a(k) = x and (a(k-1) = y or a(k+1) = y).

a(2*k^2 + k + 1) = a(A084849(k)) = 1 for k >= 0;

a(2*k^2 - 3*k) = a(A014107(k)) = 2 for k > 1;

a(2*k^2 + 5*k) = a(A033537(k)) = 3 for k > 1;

a(2*k^2 + k - 5) = a(A100040(k)) = 4 for k > 2;

a(2*k^2 + k - 7) = a(A100041(k)) = 5 for k > 3.

LINKS

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

EXAMPLE

First terms (10 = A, 11 = B, 12 = C) and some subsequences = A000027:

1231435425165764736271879869584938291A9BA8B7A6B5A4B3A2B1CBD

123.4.5....6.7........8.9............A.B................C.D.

...1....2........3............4................5..........