The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A063827 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A063827

a(n) = round(sqrt(a(n-2)^2 + a(n-1)^2)) with a(0) = 1 and a(1) = 2.
(history; published version)

#12 by Harvey P. Dale at Wed Dec 18 19:45:48 EST 2024

STATUS

editing

approved

#11 by Harvey P. Dale at Wed Dec 18 19:45:46 EST 2024

MATHEMATICA

nxt[{a_, b_}]:={b, Round[Sqrt[a^2+b^2]]}; NestList[nxt, {1, 2}, 50][[;; , 1]] (* Harvey P. Dale, Dec 18 2024 *)

STATUS

approved

editing

#10 by Bruno Berselli at Mon Jun 25 03:22:55 EDT 2018

STATUS

proposed

approved

#9 by Michel Marcus at Mon Jun 25 01:41:45 EDT 2018

STATUS

editing

proposed

#8 by Michel Marcus at Mon Jun 25 01:41:40 EDT 2018

COMMENTS

a(n)/a(n-1) tends towards 1.27201964951... = sqrt((1+sqrt(5))/2). See A139339.

CROSSREFS

Cf. A000283, A139339.

STATUS

proposed

editing

#7 by Jon E. Schoenfield at Sun Jun 24 23:40:25 EDT 2018

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sun Jun 24 23:40:23 EDT 2018

NAME

a(n) = round[(sqrt(a(n-2)^2 + a(n-1)^2)] ) with a(0) = 1 and a(1) = 2.

COMMENTS

a(n)/a(n-1) tends towards 1.27201964951... = sqrt((1+sqrt(5))/2).

LINKS

Harry J. Smith, <a href="/A063827/b063827.txt">Table of n, a(n) for n = 0,...,500</a>

EXAMPLE

a(7) = 8 since round[(sqrt(5^2 + 6^2)] ) = round[(sqrt(61)] ) = round[(7.8102...] ) = 8.

PROG

(PARI) { default(realprecision, 50); for (n=0, 500, if (n>1, a=round(sqrt(a2^2 + a1^2)); a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b063827.txt", n, " ", a) ) } [From _\\ _Harry J. Smith_, Sep 01 2009]

EXTENSIONS

Missing ) parenthesis added to definition by Harry J. Smith, Sep 01 2009

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:51:34 EDT 2012

AUTHOR

_Henry Bottomley (se16(AT)btinternet.com), _, Aug 20 2001

Discussion

Fri Mar 30

18:51

OEIS Server: https://oeis.org/edit/global/247

#4 by Russ Cox at Fri Mar 30 17:24:25 EDT 2012

PROG

(PARI) { default(realprecision, 50); for (n=0, 500, if (n>1, a=round(sqrt(a2^2 + a1^2)); a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b063827.txt", n, " ", a) ) } [From _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Sep 01 2009]

EXTENSIONS

Missing ) added to definition by _Harry J. Smith (hjsmithh(AT)sbcglobal.net), _, Sep 01 2009

Discussion

Fri Mar 30

17:24

OEIS Server: https://oeis.org/edit/global/133

#3 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

Harry J. Smith, <a href="/A063827/b063827.txt">Table of n, a(n) for n=0,...,500</a>

KEYWORD

nonn,new

nonn