The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A175885

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A175885

Numbers that are congruent to {1, 10} mod 11.
(history; published version)

#45 by Joerg Arndt at Sun Nov 24 01:52:12 EST 2024

STATUS

proposed

approved

#44 by Amiram Eldar at Sun Nov 24 00:56:42 EST 2024

STATUS

editing

proposed

#43 by Amiram Eldar at Sat Nov 23 23:50:35 EST 2024

FORMULA

From Amiram Eldar, Nov 23 2024: (Start)

Product_{n>=1} (1 - (-1)^n/a(n)) = 2*cos(Pi/11).

Product_{n>=2} (1 + (-1)^n/a(n)) = (Pi/11)*cosec(Pi/11). (End)

STATUS

approved

editing

#42 by Michael De Vlieger at Mon Sep 05 09:10:52 EDT 2022

STATUS

reviewed

approved

#41 by Michel Marcus at Mon Sep 05 01:57:49 EDT 2022

STATUS

proposed

reviewed

#40 by Jon E. Schoenfield at Sun Sep 04 22:24:14 EDT 2022

STATUS

editing

proposed

#39 by Jon E. Schoenfield at Sun Sep 04 22:24:13 EDT 2022

COMMENTS

Cf. property described by _Gary Detlefs _ in A113801: more generally, these numbers are of the form (2*h*n + (h-4)*(-1)^n - h)/4 (h, n natural numbers), therefore ((2*h*n + (h-4)*(-1)^n - h)/4)^2 - 1 == 0 (mod h); in this case, a(n)^2 - 1 == 0 (mod 11).

FORMULA

a(n) = (22*n + 7*(-1)^n - 11)/4.

a(n) = -a(-n+1) = a(n-2) + 11 = a(n-1) + a(n-2) - a(n-3).

a(n) = 11*A000217(n-1) + 1 - 2*Sum_{i=1..n-1} a(i) for n > 1.

a(n) = A195312(n) + A195312(n-1) = A195313(n) - A195313(n-2). - Bruno Berselli, Sep 18 2011

STATUS

proposed

editing

#38 by David Lovler at Sun Sep 04 20:55:30 EDT 2022

STATUS

editing

proposed

#37 by David Lovler at Sun Sep 04 12:19:55 EDT 2022

FORMULA

E.g.f.: 1 + ((22*x - 11)*exp(x) + 7*exp(-x))/4. - David Lovler, Sep 04 2022

PROG

(MAGMAMagma) [(22*n+7*(-1)^n-11)/4: n in [1..60]]; // Vincenzo Librandi, Sep 19 2011

STATUS

approved

editing

#36 by Peter Luschny at Sat Dec 04 04:46:30 EST 2021

STATUS

reviewed

approved