A306389 Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).

-3, -2, -6, -5, -10, -1, -3, 3, -2, 1, -4, 4, -5, 2, -7, -4, -6, -3, -11, -7, -13, -11, -17, -13, -16, -13, -21, -18, -20, -13, -22, -17, -17, -15, -23, -15, -19, -18, -27, -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

Offset: 1

Author

Luca Petrone, Feb 12 2019

Keywords

• sign
• base
• easy

Comments

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

Crossrefs

Cf. A000796, A046974, A099816, A099817.

Programs

Mathematica

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

Formula

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

a(n) = Sum_{k=1..floor(n/2)} A099817(k) - Sum_{k=1..floor((n+1)/2)} A099816(k). - Michel Marcus, Feb 16 2019