login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A354222
Decimal expansion of 2 / (Pi+2).
0
3, 8, 8, 9, 8, 4, 5, 2, 9, 6, 4, 8, 3, 4, 2, 7, 1, 0, 6, 1, 9, 4, 0, 4, 6, 1, 2, 0, 4, 6, 0, 3, 1, 1, 3, 8, 2, 6, 2, 5, 7, 7, 3, 6, 7, 0, 4, 3, 9, 0, 7, 2, 0, 4, 7, 9, 1, 0, 8, 3, 2, 2, 4, 9, 5, 7, 5, 3, 5, 1, 6, 6, 0, 6, 3, 6, 8, 4, 1, 6, 1, 3, 4, 2, 6, 2, 8, 6, 1, 6, 5, 4, 3, 3, 2, 5, 6, 9, 4, 0
OFFSET
0,1
COMMENTS
The sequence u(n+1) = 1 / ( u(n) + 1/(n+1) ) with u(0) >= 0 is convergent with lim_{n->oo} u(n) = 1; however, this sequence is monotonic iff u(0) = 2 / (Pi+2), and in this case, this sequence is increasing.
REFERENCES
J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, 1993, Exercice 1, pp. 29-35.
FORMULA
Equals 1 - A197686.
EXAMPLE
0.388984529648342710619404612046031138262577367...
MAPLE
evalf(2/(Pi+2), 100);
MATHEMATICA
RealDigits[2/(Pi + 2), 10, 100][[1]] (* Amiram Eldar, May 19 2022 *)
PROG
(PARI) 2/(Pi+2) \\ Michel Marcus, May 20 2022
CROSSREFS
Sequence in context: A371137 A140975 A065481 * A032538 A168209 A305513
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, May 19 2022
STATUS
approved