A112416 - OEIS

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A112416

Next-to-most-significant binary digit of the n-th prime.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The length of the run of zeros pi(2^n+2^(n-1))-pi(2^n) (A095765): 1, 1, 1, 3, 4, 6, 12, 22, 38, 70, 130, 237, 441, ... and the length of the run of ones pi(2^n-1)-pi(2^n-2^(n-2)-1) (A095766): 1, 1, 1, 2, 3, 7, 11, 21, 37, 67, 125, 227, 431, ..., . - Robert G. Wilson v

LINKS

Table of n, a(n) for n=1..105.

FORMULA

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

EXAMPLE

The 9th prime is 23 (in decimal), which is 10111 in binary. So a(9) = 0, the next-to-most significant binary digit of 23.

MATHEMATICA

f[n_] := IntegerDigits[Prime@n, 2][[2]]; Array[f, 105] (* Robert G. Wilson v *)

CROSSREFS

Cf. A004676, A106701.

Sequence in context: A268384 A358670 A288524 * A061265 A288466 A285073

Adjacent sequences: A112413 A112414 A112415 * A112417 A112418 A112419