id:A069210 - OEIS Search Results

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a(1)=a(2)=1, a(n+2)=a(n+1)+1 if sign(Sinus(a(n+1))=sign(Sinus(a(n)), a(n+2)=a(n)+1 otherwise.

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1, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53, 54, 54, 55 (list; graph; listen)

	OFFSET	`1,3`
	COMMENT	`Asymptotically a(n)~Cn with C=0.75854... Is this constant rational?` `The constant C=0.75854... isn't rational. Otherwise it would imply the rationality of Pi since C=Pi/(Pi+1)=0.7585469930... For n>=6 we have a(n)=(n-1)-k with k>=1 such that ceil(k(Pi+1)) <= (n-1) < ceil((k+1)(Pi+1)) = ceil(k(Pi+1)) + 4 or 5. So n-1 = k(Pi+1) + O(1) and then: a(n)=(Pi/(Pi + 1))n + O(1). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 15 2002`
	CROSSREFS	`Sequence in context: A123580 A072894 A037915 this_sequence A006162 A036701 A053756` `Adjacent sequences: A069207 A069208 A069209 this_sequence A069211 A069212 A069213`
	KEYWORD	`easy,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 11 2002`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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