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

Author

Will Nicholes, Jun 06 2010

Keywords

• base
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A004601, A050279.

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

Programs

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 *)

Extensions

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