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Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).
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%I #24 Dec 04 2024 18:50:47

%S -3,-2,-6,-5,-10,-1,-3,3,-2,1,-4,4,-5,2,-7,-4,-6,-3,-11,-7,-13,-11,

%T -17,-13,-16,-13,-21,-18,-20,-13,-22,-17,-17,-15,-23,-15,-19,-18,-27,

%U -20,-21,-15,-24,-21,-30,-21,-24,-17,-22,-21,-21,-16,-24,-22,-22,-13,-20,-16,-25,-21,-25,-20,-29,-27,-30,-30,-37,-29,-30,-24,-28

%N Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).

%C a(n) > 0 for n = 8, 10, 12, 14, 16124, 16126, ... and a(n) = 0 for n = 16120, 16161, 16937, ... - _Michel Marcus_, Feb 13 2019

%F a(n) = Sum_{k=1..n} (-1)^k*A000796(k).

%F a(n) = Sum_{k=1..floor(n/2)} A099817(k) - Sum_{k=1..floor((n+1)/2)} A099816(k). - _Michel Marcus_, Feb 16 2019

%t Accumulate@ MapIndexed[(-1)^First[#2]*#1 &, First@ RealDigits[Pi, 10, 71]] (* _Michael De Vlieger_, Feb 15 2019 *)

%Y Cf. A000796, A046974, A099816, A099817.

%K sign,base,easy

%O 1,1

%A _Luca Petrone_, Feb 12 2019