1,3

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.

In contrast to A378472, this sequence does not require the length of the run of 0s to be exactly n, more 0s may follow. - M. F. Hasler, Feb 04 2026

Pi's binary expansion is 11.00100100001111110110101010001..., so the strings '0' and also '00' occur first at position a(1) = a(2) = 1 in the fractional part, and the strings '000' and '0000' occur first at position a(3) = a(4) = 7. - M. F. Hasler, Feb 04 2026

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.

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 *)

Cf. A004601, A050279.

Cf. A178709.

Cf. A378472 (start of a string of exactly n 0s).

Sequence in context: A269902 A269937 A065240 * A072399 A001988 A099739

Adjacent sequences: A178705 A178706 A178707 * A178709 A178710 A178711

base,nonn,more

Will Nicholes, Jun 06 2010

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

a(28)-a(31) from Michael S. Branicky, Feb 04 2026

approved