A004603 Expansion of Pi in base 4.

3, 0, 2, 1, 0, 0, 3, 3, 3, 1, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 1, 2, 2, 0, 3, 0, 0, 2, 0, 3, 1, 0, 3, 0, 1, 0, 3, 0, 1, 2, 1, 2, 0, 2, 2, 0, 2, 3, 2, 0, 0, 0, 3, 1, 3, 0, 0, 1, 3, 0, 3, 1, 0, 1, 0, 2, 2, 1, 0, 0, 0, 2, 1, 0, 3, 2, 0, 0, 2, 0, 2, 0, 2, 2, 1, 2, 1, 3, 3, 0, 3, 0, 1, 3, 1, 0, 0, 0, 0, 2, 0, 0, 2, 3, 2

Offset

1,1

Comments

Theoretically, this sequence could be used to encode a given number of digits of Pi as a DNA sequence, which could then be read back from one helix. The value read back from the other helix would of course depend on the assignment of G, A, C, T to the digits 0, 1, 2, 3. - Alonso del Arte, Nov 07 2011

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Francisco Javier Aragón Artacho, 100 billion step walk on the digits of pi

F. J. Aragon Artacho, D. H. Bailey, J. M. Borwein, P. B. Borwein, J. Fountain, and M. Skerritt Walking on numbers: a multiple media mathematics project, 2012.

Elias Bröms, Pictures of Pi

Formula

a(n) = 2*A004601(2n) + A004601(2n+1). - Jason Kimberley, Nov 08 2012

Example

3.02100333122220202011220300203103010301...

Mathematica

RealDigits[Pi, 4, 100][[1]]
Table[ResourceFunction["NthDigit"][Pi, n, 4], {n, 1, 100}] (* Joan Ludevid, Jul 04 2022; easy to compute a(10000000)=2 with this function; requires Mathematica 12.0+ *)

Crossrefs

Pi in base b: A004601 (b=2), A004602 (b=3), this sequence (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9), A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).

Cf. A007514.

Cf. A004595, A004541. - Jason Kimberley, Dec 01 2012

Sequence in context: A124452 A351532 A291786 * A174951 A275326 A092926

Adjacent sequences: A004600 A004601 A004602 * A004604 A004605 A004606

Keyword

nonn,base,cons,easy

Author

N. J. A. Sloane

Status

approved