id:A100035 - OEIS Search Results

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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.

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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 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`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(k-1)=y) or a(k+1)=y);` `a(2k^2 + k + 1) = a(A084849(k)) = 1 for k>=0;` `a(2k^2 - 3k) = a(A014107(k)) = 2 for k>1;` `a(2k^2 + 5k) = a(A033537(k)) = 3 for k>1;` `a(2k^2 + k - 5) = a(A100040(k)) = 4 for k>2;` `a(2*k^2 + k - 7) = a(A100041(k)) = 5 for k>3;`
	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: A095701 A067992 A140757 this_sequence A090244 A096180 A034867` `Adjacent sequences: A100032 A100033 A100034 this_sequence A100036 A100037 A100038`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 31 2004`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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