A106701 a(n) = next-to-most-significant binary digit of n-th composite positive integer.

0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Leroy Quet, Jan 22 2006

Keywords

• base
• nonn

Comments

The length of each run of zeros and ones: 1,3,6,13,25,53,107,219,445,899,1821,... and 1,3,5,12,26,52,106,218,442,894,1811,2838,..., . - Robert G. Wilson v

Examples

			a(2) = 1 because 6 is the second composite and because the next-to-most-significant binary digit (which happens to be the middle binary digit) of 6 = 110 (in binary) is 1.
		

Crossrefs

Cf. A115454, A112416.

Programs

Mathematica

f[n_] := IntegerDigits[ FixedPoint[n + PrimePi[ # ] + 1 &, n], 2][[2]]; Array[f, 105] (* Robert G. Wilson v *)

Formula

a(n) = floor((c(n) - 2^m)/2^(m-1)), where c(n) is the n-th composite and m = floor(log(c(n))/log(2)).

Extensions

More terms from Robert G. Wilson v, Jan 24 2006