A080276 Variation on Connell sequence (A001614). In this one, a(1)=1, terms a(n) onwards are generated in "blocks" as the next a(n-1) odd numbers > a(n-1) if the previous block ends with a(n-1) even and the next a(n-1) even numbers > a(n-1) if the previous block ends with a(n-1) odd.

1, 2, 3, 5, 6, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 123, 125

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003

Keywords

• nonn

Comments

The entries at the end of each odd or even block are 1,2,5,14,41,122,363,... and the first differences of these are 1,3,9,27,81,241=powers of 3.

Examples

			a(4)=5, which is odd, so the next terms from a(5) onwards are the next 5 even numbers greater than 5: 6,8,10,12,14. Thus the term 14 is followed by the next 14 odd numbers: 15,17,...,41 and so on.
		

Crossrefs

Cf. A001614.

Formula

a(n) = round( LambertW(3^((4*n-3)/2)*log(3)/2)/log(3)) = round( LambertW(x*exp((4*n-3)*x))/(2*x) ), where x=log(sqrt(3)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 13 2003