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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).
0
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, ...
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 A376105 A349653
KEYWORD
nonn
AUTHOR
Arthur Lenskold, Apr 20 2021
EXTENSIONS
More terms from Michel Marcus, Apr 23 2021
STATUS
approved