A178708 Position of start of first appearance of n consecutive 0's in the binary expansion of Pi.

1, 1, 7, 7, 96, 96, 96, 189, 902, 902, 4267, 8375, 8375, 8375, 11791, 11791, 112954, 436893, 726844, 726844, 2005750, 2005750, 2005750, 42248747, 171498580, 171498580, 171498580

Offset

1,3

Comments

In the first 2^28 binary digits, 134220460 are "0" and 134214996 are "1". - Robert G. Wilson v, Jun 09 2010

This sequence ignores bits in the integer part of the binary expansion of Pi.

Links

Table of n, a(n) for n=1..27.

Example

3 consecutive 0's are first found beginning at the 7th position in Pi's binary expansion, so the third term in this sequence is 7.

Mathematica

pib = ToString@ FromDigits[ RealDigits[Pi - 3, 2, 2^26][[1]]]; f[n_] := 3 + StringPosition[ pib, ToString[10^n], 1][[1, 1]]; f[1] = f[2] = 1; Array[f, 27] (* Robert G. Wilson v, Jun 09 2010 *)
With[{p=RealDigits[Pi, 2, 1715*10^5][[1]]}, Flatten[Table[SequencePosition[ p, PadRight[{}, n, 0], 1], {n, 27}], 1][[All, 1]]-2] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 26 2019 *)

Crossrefs

Cf. A004601, A050279.

Cf. A178709. - Robert G. Wilson v, Jun 09 2010

Sequence in context: A269902 A269937 A065240 * A072399 A001988 A099739

Adjacent sequences: A178705 A178706 A178707 * A178709 A178710 A178711

Keyword

base,nonn

Author

Will Nicholes, Jun 06 2010

Extensions

a(17)-a(27) from Robert G. Wilson v, Jun 09 2010

Status

approved