A343572 a(n) = ceiling((16^n)*Sum_{k=0..n+1} (4/(8k+1)-2/(8k+4)-1/(8k+5)-1/(8k+6))/16^k).

4, 51, 805, 12868, 205888, 3294199, 52707179, 843314857, 13493037705, 215888603273, 3454217652358, 55267482437723, 884279719003556, 14148475504056881, 226375608064910089, 3622009729038561422, 57952155664616982740, 927234490633871723826, 14835751850141947581204

Offset

0,1

Comments

The formula gives an approximation to 16^n*Pi. The first 300 terms agree with ceiling(16^n*Pi) but this may not be true in general.

Terms in base 16 are 4, 33, 325, 3244, 32440, 3243F7, 3243F6B, 3243F6A9, 3243F6A89, 3243F6A889, 3243F6A8886, 3243F6A8885B, 3243F6A8885A4, 3243F6A8885A31, 3243F6A8885A309, 3243F6A8885A308E, 3243F6A8885A308D4, 3243F6A8885A308D32, 3243F6A8885A308D314, 3243F6A8885A308D3132, ...

Links

Table of n, a(n) for n=0..18.

William Blankenship, First 8366 HEX digits of pi

Wikipedia, Bailey-Borwein-Plouffe formula

Formula

a(n) = ceiling((16^n)*Sum_{k=0..n+1} (4/(8k+1)-2/(8k+4)-1/(8k+5)-1/(8k+6))/16^k).

Mathematica

Array[Ceiling[(16^#)*Sum[(4/(8 k + 1) - 2/(8 k + 4) - 1/(8 k + 5) - 1/(8 k + 6))/16^k, {k, 0, # + 1}]] &, 19, 0] (* Michael De Vlieger, May 01 2021 *)

Prog

(PARI) a(n) = ceil((16^n)*sum(k=0, n+1, (4/(8*k+1)-2/(8*k+4)-1/(8*k+5)-1/(8*k+6))/16^k)); \\ Michel Marcus, Apr 23 2021

Crossrefs

Cf. A000796.

Sequence in context: A320645 A347921 A328931 * A336608 A349653 A235325

Adjacent sequences: A343569 A343570 A343571 * A343573 A343574 A343575

Keyword

nonn

Author

Arthur Lenskold, Apr 20 2021

Extensions

More terms from Michel Marcus, Apr 23 2021

Status

approved