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A302342
Cumulative sums of the bits in the binary representation of Pi.
1
1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 19, 20, 20, 21, 21, 21, 21, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 26, 26, 27, 27, 27, 28, 29, 29, 29, 29
OFFSET
-1,2
COMMENTS
The leading binary bits of Pi are 11.0010010000111111011010101000100010000101101000110000100011010011000...
FORMULA
a(n) = sum of the bits with value 2^(-n) or larger.
a(n) = (A166006(n+2) + n + 2)/2. - Pontus von Brömssen, Nov 26 2020
MATHEMATICA
Accumulate[First[RealDigits[Pi, 2, 100]]] (* Paolo Xausa, Jul 31 2024 *)
CROSSREFS
Partial sums of A004601.
A256108 is the sequence of -1 followed by those values of n for which a(n) is strictly greater than a(n-1).
Cf. A166006.
Sequence in context: A375433 A046155 A026819 * A137214 A284726 A319951
KEYWORD
nonn,base
AUTHOR
Lee A. Newberg, Apr 05 2018
STATUS
approved