The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A055792 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A055792

a(n) and floor(a(n)/2) are both squares; i.e., squares which remain squares when written in base 2 and last digit is removed.
(history; published version)

#48 by Peter Luschny at Mon Jul 22 05:32:32 EDT 2024

STATUS

proposed

approved

#47 by Paolo Xausa at Mon Jul 22 05:24:32 EDT 2024

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editing

proposed

#46 by Paolo Xausa at Mon Jul 22 05:24:14 EDT 2024

MATHEMATICA

LinearRecurrence[{35, -35, 1}, {0, 1, 9, 289}, 25] (* Paolo Xausa, Jul 22 2024 *)

STATUS

approved

editing

#45 by Joerg Arndt at Sat Jan 21 02:25:28 EST 2023

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reviewed

approved

#44 by Michel Marcus at Sat Jan 21 01:13:44 EST 2023

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proposed

reviewed

#43 by Jon E. Schoenfield at Fri Jan 20 18:12:50 EST 2023

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editing

proposed

#42 by Jon E. Schoenfield at Fri Jan 20 18:12:48 EST 2023

FORMULA

From Colin Barker, Sep 15 2014: (Start)

a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3) for n > 3. G.f.: -x*(9*x^2-26*x+1) / ((x-1)*(x^2-34*x+1)). - _Colin Barker_, Sep 15 2014

G.f.: -x*(9*x^2 - 26*x + 1) / ((x-1)*(x^2 - 34*x + 1)). (End)

a(n) = (4 + 2*(17 + 12*sqrt(2))^(1-n) + (34 - 24*sqrt(2))*(17 + 12*sqrt(2))^n)/8 for n > 0. - Colin Barker, Mar 02 2016

EXAMPLE

a(2) = 9 because 9 = 3^2 = 1001 base _2 and 100 base _2 = 4 = 2^2.

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proposed

editing

#41 by Michael De Vlieger at Fri Jan 20 18:02:09 EST 2023

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editing

proposed

#40 by Michael De Vlieger at Fri Jan 20 18:02:07 EST 2023

LINKS

Giovanni Lucca, <a href="https://ijgeometry.com/product/giovanni-lucca-circle-chains-inside-the-arbelos-and-integer-sequences/">Circle chains inside the arbelos and integer sequences</a>, Int'l J. Geom. (2023) Vol. 12, No. 1, 71-82.

STATUS

approved

editing

#39 by N. J. A. Sloane at Thu Jun 14 11:46:24 EDT 2018

STATUS

proposed

approved