The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A146348 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A146348

Primes p such that continued fraction of (1 + sqrt(p))/2 has period 3.
(history; published version)

#29 by OEIS Server at Mon Mar 30 08:36:53 EDT 2020

LINKS

Amiram Eldar, <a href="/A146348/b146348_1.txt">Table of n, a(n) for n = 1..2500</a> (terms 1..200 from Zak Seidov)

#28 by Joerg Arndt at Mon Mar 30 08:36:53 EDT 2020

STATUS

reviewed

approved

Discussion

Mon Mar 30

08:36

OEIS Server: Installed new b-file as b146348.txt.  Old b-file is now b146348_1.txt.

#27 by Michel Marcus at Mon Mar 30 04:31:13 EDT 2020

STATUS

proposed

reviewed

#26 by Amiram Eldar at Mon Mar 30 04:30:14 EDT 2020

STATUS

editing

proposed

#25 by Amiram Eldar at Mon Mar 30 03:33:47 EDT 2020

NAME

Primes p such that continued fraction of (1 + sqrt(p))/2 has period 3.

#24 by Amiram Eldar at Mon Mar 30 02:17:25 EDT 2020

LINKS

Amiram Eldar, <a href="/A146348/b146348_1.txt">Table of n, a(n) for n = 1..2500</a> (terms 1..200 from Zak Seidov)

#23 by Amiram Eldar at Mon Mar 30 02:16:58 EDT 2020

LINKS

Zak Seidov, Amiram Eldar, <a href="/A146348/b146348_1.txt">Table of n, a(n) for n = 1..2002500</a>

STATUS

approved

editing

#22 by Jon E. Schoenfield at Sat Oct 19 22:39:09 EDT 2019

STATUS

editing

approved

#21 by Jon E. Schoenfield at Sat Oct 19 22:38:57 EDT 2019

COMMENTS

The primes of the form p = n^2+1 for n>2 are in the sequence, and the continued fraction of (1+sqrt(p))/2 is [n/2; 1, 1, n-1, 1, 1, n-1, 1, 1, ...] with the period (1, 1, n-1).

We observe that the other primes {61, 317, 461, 557, 773, 1129, 1429,… ...} are prime divisors of composites numbers of the form k^2+1 where k = 11, 114, 48, 118, 317, 168, 620,… ... .

STATUS

approved

editing

#20 by N. J. A. Sloane at Sat Sep 06 00:39:47 EDT 2014

STATUS

proposed

approved