A351222 Decimal expansion of Sum_{k>=0} (-1)^k/Fibonacci(4*k+2).

8, 9, 0, 8, 6, 7, 0, 2, 1, 9, 7, 2, 1, 1, 8, 2, 6, 0, 0, 4, 8, 8, 5, 1, 5, 2, 9, 2, 4, 1, 5, 6, 8, 0, 2, 0, 4, 3, 0, 5, 1, 2, 8, 4, 4, 1, 5, 8, 2, 0, 4, 3, 4, 5, 6, 6, 2, 0, 8, 0, 2, 7, 1, 9, 7, 5, 5, 2, 1, 5, 5, 6, 7, 2, 2, 1, 9, 9, 7, 5, 7, 6, 0, 5, 3, 1, 7, 8, 8, 3, 4, 9, 1, 6, 6, 2, 6, 7, 9, 5, 8, 5, 9, 2, 6

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Wray G. Brady, Problem B-319, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 13, No. 4 (1975), p. 373; Rerun, Solution to Problem B-319, ibid., Vol. 14, No. 5 (1976), p. 472.

L. Carlitz, Problem B-111, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 5, No. 1 (1967), p. 108; Another Series Equality, Solution to Problem B-110 by the proposer, ibid., Vol. 5, No. 5 (1967), pp. 470-471.

Formula

Equals sqrt(5) * Sum_{k>=0} 1/Lucas(4*k+2) (Carlitz, 1967).

Example

0.89086702197211826004885152924156802043051284415820...

Mathematica

RealDigits[NSum[(-1)^n/Fibonacci[4*n + 2], {n, 0, Infinity}, WorkingPrecision -> 1200], 10, 100][[1]]

Prog

(PARI) sumpos(k=0, (-1)^k/fibonacci(4*k+2)) \\ Michel Marcus, Feb 05 2022

Crossrefs

Cf. A000032, A000045, A033890, A246453.

Sequence in context: A021845 A133747 A222458 * A370093 A019872 A011421

Adjacent sequences: A351219 A351220 A351221 * A351223 A351224 A351225

Keyword

nonn,cons

Author

Amiram Eldar, Feb 05 2022

Status

approved