A069210 a(1)=a(2)=1, a(n+2) = a(n+1)+1 if sign(sin(a(n+1))) = sign(sin(a(n))), a(n+2) = a(n)+1 otherwise.

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

Offset

1,3

Comments

Asymptotically a(n)~C*n with C=0.75854... Is this constant rational?

The constant C=0.75854... is not 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 ceiling(k*(Pi+1)) <= (n-1) < ceiling((k+1)*(Pi+1)) = ceiling(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

Links

Table of n, a(n) for n=1..73.

Crossrefs

Sequence in context: A328309 A037915 A195180 * A195172 A367193 A277425

Adjacent sequences: A069207 A069208 A069209 * A069211 A069212 A069213

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 11 2002

Status

approved