A065828 Binary digits found in the decimal expansion of Pi, listed with repetitions and in order of appearance.

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

Offset

1

Comments

If Pi is normal then every possible string of 0's and 1's will appear in this sequence. - Joshua Oliver, Nov 27 2019

The condition of normality is much stronger than required for this result, which is already a consequence of the digit sequence being disjunctive. But even that is much stronger than required, because it would mean that any binary string appears as a substring in the (decimal!) digits of Pi, not just as a subsequence, which is all that is required for any binary string to appear here (where all digits > 1 are deleted), even infinitely often. - M. F. Hasler, Feb 04 2026

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000 (terms 1..7641 from Felix Fröhlich)

Example

From Felix Fröhlich, Nov 27 2019: (Start)
The first of the following lines shows the decimal expansion of Pi and the second the expansion with all digits except 0 and 1 omitted, thus giving the terms of the sequence:
3.1415926535897932384626433832795028841971693993751058209749445923078164062
  1 1                            0    1  1        10   0          0  1  0
(End)

Mathematica

Select[ RealDigits[Pi, 10, 520][[1]], # < 2 &] (* Robert G. Wilson v, May 04 2009 *)

Prog

(PARI) my(d=digits(floor(Pi*10^400))); for(k=1, #d, if(d[k] < 2, print1(d[k], ", "))) \\ Felix Fröhlich, Nov 27 2019

Crossrefs

Cf. A000796, A011545, A011546, A055143, A065829 - A065840.

Sequence in context: A374039 A014114 A014219 * A341603 A190897 A176329

Adjacent sequences: A065825 A065826 A065827 * A065829 A065830 A065831

Keyword

nonn,base

Author

Patrick De Geest, Nov 24 2001

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 31 2021

Status

approved