The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A145277

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A145277

a(n) = A145234(n+1)/A145234(n).
(history; published version)

#9 by OEIS Server at Wed Oct 23 16:33:19 EDT 2024

LINKS

Amiram Eldar, <a href="/A145277/b145277_1.txt">Table of n, a(n) for n = 1..3</a>

#8 by Michael De Vlieger at Wed Oct 23 16:33:19 EDT 2024

STATUS

reviewed

approved

Discussion

Wed Oct 23

16:33

OEIS Server: Installed first b-file as b145277.txt.

#7 by Andrew Howroyd at Wed Oct 23 15:41:39 EDT 2024

STATUS

proposed

reviewed

#6 by Amiram Eldar at Wed Oct 23 03:06:22 EDT 2024

STATUS

editing

proposed

#5 by Amiram Eldar at Wed Oct 23 02:33:19 EDT 2024

CROSSREFS

Cf. A001566, A001622, A002814, A145234, A145274, A145275, A145276.

#4 by Amiram Eldar at Wed Oct 23 02:32:51 EDT 2024

NAME

a(n) = A145234(n+1)/A145234(n).

COMMENTS

(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + Sqrt[sqrt(5]))/2

For k=2 see A001566.

For k=3 see A002814(n+2).

For k=4 see A145274.

For k=5 see A145275.

For k=6 see A145276.

For k=7 see A145277this sequence.

FORMULA

a(n) = (G^(7^(n + 1)) - (1 - G)^(7^(n + 1)))/(G^(7^n) - (1 - G)^(7^n)) where G = (1 + Sqrt[sqrt(5]))/2.

MATHEMATICA

G = (1 + Sqrt[5])/2; Table[Expand[(G^(7^(n + 1)) - (1 - G)^(7^(n + 1)))/Sqrt[5]]/Expand[(G^(7^n) - (1 - G)^(7^n))/Sqrt[5]], {n, 1, 5}] (*Artur Jasinski*)

CROSSREFS

Cf. A001566, A002814, A145234, A145274, A145275, A145276, A145277.

#3 by Amiram Eldar at Wed Oct 23 02:31:30 EDT 2024

LINKS

Amiram Eldar, <a href="/A145277/b145277_1.txt">Table of n, a(n) for n = 1..3</a>

STATUS

approved

editing

#2 by Russ Cox at Sat Mar 31 10:22:10 EDT 2012

AUTHOR

_Artur Jasinski (grafix(AT)csl.pl), _, Oct 06 2008

Discussion

Sat Mar 31

10:22

OEIS Server: https://oeis.org/edit/global/339

#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

NAME

a(n)=A145234(n+1)/A145234(n)

DATA

598364773, 27692759465311176949233529747775189817301578781117871380248013

OFFSET

1,1

COMMENTS

A member of the family of sequences of type:

(G^(k^(n + 1)) - (1 - G)^(k^(n + 1)))/(G^(k^n) - (1 - G)^(k^n)) where G = (1 + Sqrt[5])/2

k=2 see A001566

k=3 see A002814(n+2)

k=4 see A145274

k=5 see A145275

k=6 see A145276

k=7 see A145277

FORMULA

a(n)=(G^(7^(n + 1)) - (1 - G)^(7^(n + 1)))/(G^(7^n) - (1 - G)^(7^n)) where G = (1 + Sqrt[5])/2

MATHEMATICA

G = (1 + Sqrt[5])/2; Table[Expand[(G^(7^(n + 1)) - (1 - G)^(7^(n + 1)))/Sqrt[5]]/Expand[(G^(7^n) - (1 - G)^(7^n))/Sqrt[5]], {n, 1, 5}] (*Artur Jasinski*)

CROSSREFS

A001566, A002814, A145274, A145275, A145276, A145277

KEYWORD

nonn,bref

AUTHOR

Artur Jasinski (grafix(AT)csl.pl), Oct 06 2008

STATUS

approved