A338157 Numbers that follow from the alternating series a(n) = d(1) - d(2) + d(3) -d(4) + ... + (-1)^(n+1) d(n), where d(k) denotes the k-th term of the digit sequence of the Golden Ratio.

1, -5, -4, -12, -12, -15, -12, -21, -13, -21, -14, -18, -9, -17, -8, -12, -4, -8, 0, -2, -2, -6, -1, -9, -3, -11, -8, -12, -9, -15, -10, -16, -13, -21, -20, -21, -14, -21, -19, -19, -16, -16, -7, -8, -1, -10, -2, -2, 3, -4, 2, 0, 8, 2

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Formula

a(1) = d(1) = 2; a(n) = a(n-1) + (-1)^(n+1) d(n) for n > 1.

Example

a(3) = d(1) - d(2) + d(3) = 1 - 6 + 1 = -4.

Mathematica

S[X_, n_] :=
Accumulate[(-1)^Range[0, n - 1]*RealDigits[X, 10, n][[1]]]
S[GoldenRatio, 54] (*This generates the first 54 elements of this sequence*)

Crossrefs

Cf. A001622 (Golden Ratio), A069159 (similar sequence for Pi), A338108 (similar sequence for Euler's number).

Sequence in context: A095871 A284551 A316671 * A189235 A019068 A215947

Adjacent sequences: A338154 A338155 A338156 * A338158 A338159 A338160

Keyword

base,easy,sign,less

Author

Dirk Broeders, Oct 14 2020

Status

approved