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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• cons
• easy

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

Examples

			3.02100333122220202011220300203103010301...
		

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

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

Programs

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+ *)

Formula

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