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A199693 Related to the expansion of Pi in base 2 (A004601). 0

%I

%S 12,4,16,126,6,2,2,8,8,16,2,6,8,48,8,6,4,24,4,24,12,24,2,8,2,896,6,

%T 224,28,6,8,4,2,4,64,4,4,224,8,8,2,4,12,124,24,14,256,32,2,14,62,2,4,

%U 24,14,24,4,28,6,12,8,4,2,8,2,4,2,32,16,60,24,56,6

%N Related to the expansion of Pi in base 2 (A004601).

%C A004601 is the concatenation of binary digits of the terms written in base 2.

%e A004601( expansion of Pi in base 2) :

%e 1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0.... ->

%e 1,1,0,0 | 1,0,0 | 1,0,0,0,0 | 1,1,1,1,1,1,0 | 1,1,0 | 1,0 | ... ->

%e 1100 | 100 |10000 | 1111110 |110 |10 | 10 | ... (in base 2) ->

%e 12 , 4, 16, 126, 6, 2, 2, ... (in base 10) .

%t f[{a_, b_}] := (2^a - 1)*2^b; f /@ Partition[Length /@ Split[First[RealDigits[π, 2, 10^3]]], 2] (* _T. D. Noe_, Nov 09 2011 *)

%o (Python)

%o import gmpy2

%o pi = gmpy2.const_pi(precision=310) # increase precision for more terms

%o h = "{0:A}".format(pi)[2:-5].replace(".", "")

%o b = bin(int(h, 16))[2:]

%o splitb = b.replace("01", "0,1").split(",")

%o print([int(t, 2) for t in splitb[:-1]]) # _Michael S. Branicky_, Dec 04 2021

%Y Cf. A004601, A007088.

%K easy,nonn,base

%O 1,1

%A _Philippe Deléham_, Nov 09 2011

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Last modified January 27 06:18 EST 2022. Contains 350601 sequences. (Running on oeis4.)