

A100035


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


10



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 example and A100036, A100037, A100038 and A100039:
exactly one k exists for all x<y such that a(k)=x and (a(k1)=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

Table of n, a(n) for n=1..88.


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


CROSSREFS

Sequence in context: A317024 A140757 A258254 * A201927 A238442 A090244
Adjacent sequences: A100032 A100033 A100034 * A100036 A100037 A100038


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Oct 31 2004


STATUS

approved



