A346839 Decimal expansion of Sum_{n>=0} A346838(n) / n!.

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

Offset

0,1

Links

Table of n, a(n) for n=0..89.

Index entries for transcendental numbers.

Formula

Equals sec(1) - tan(1) = A073448-A049471. - Amiram Eldar, Aug 17 2021

From Peter Bala, Feb 14 2026: (Start)

Equals 1/A384932.

Simple continued fraction expansion: 1/(3 + 1/(2 + 1/(2 + 1/(4 + 1/(2 + 1/(6 + 1/(2 + 1/(8 + 1/(2 + ... ))))))))).

More generally, for integer n >= 2, the simple continued fraction expansion of sec(1/n) - tan(1/n) is 1/(1 + 1/(n-1 + 1/(2 + 1/(3*n-1 + 1/(2 + 1/(5*n-1 + 1/(2 + 1/(7*n-1 + 1/(2 + 1/(9*n-1 + ... )))))))))). (End)

Example

0.29340799302602338740477843394029002038314588271248926...

Maple

A := n -> I*(polylog(-n, -I) - exp(I*Pi*n)*polylog(-n, I)) / exp(I*Pi*n/2):
Digits := 120; sum(A(n)/n!, n = 0..infinity): evalf(%)*10^91:
ListTools:-Reverse(convert(floor(%), base, 10));

Mathematica

RealDigits[Sec[1] - Tan[1], 10 , 100][[1]] (* Amiram Eldar, Aug 17 2021 *)

Prog

(PARI) 1/cos(1) - tan(1) \\ Charles R Greathouse IV, May 11 2026

Crossrefs

Cf. A049471, A073448, A346838, A384932.

Sequence in context: A388484 A071194 A347359 * A137616 A154581 A111689

Adjacent sequences: A346836 A346837 A346838 * A346840 A346841 A346842

Keyword

nonn,cons

Author

Peter Luschny, Aug 13 2021

Status

approved