The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A053027

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A053027

Odd primes p with 2 zeros in Fibonacci numbers mod p.
(history; published version)

#39 by Michael De Vlieger at Tue Jun 25 08:30:16 EDT 2024

STATUS

proposed

approved

#38 by Jianing Song at Tue Jun 25 08:15:04 EDT 2024

STATUS

editing

proposed

#37 by Jianing Song at Tue Jun 25 08:14:24 EDT 2024

COMMENTS

For p > 2, p is in this sequence if and only if 8 divides of A001175(p), and if and only if 4 divides A001177(p). For a proof of the equivalence between A001176(p) = 2 and 4 dividing A001177(p), see Section 2 of my link below.

This sequence contains all primes congruent to 3, 7 (mod 20). This corresponds to case (2) for k = 3 in the Conclusion of Section 1 of my link below.

Conjecturely, this sequence has density 1/3 in the primes. (End) [Comment rewritten by _Jianing Song_, Jun 16 2024 and Jun 25 2024]

See my link below for general statements. (End)

STATUS

approved

editing

#36 by Michael De Vlieger at Mon Jun 17 10:49:13 EDT 2024

STATUS

proposed

approved

#35 by Jianing Song at Mon Jun 17 09:16:08 EDT 2024

STATUS

editing

proposed

#34 by Jianing Song at Mon Jun 17 09:06:55 EDT 2024

CROSSREFS

The sequence {x(n)} | A000045 | A000129 | A006190

STATUS

approved

editing

#33 by Michael De Vlieger at Mon Jun 17 08:50:46 EDT 2024

STATUS

reviewed

approved

#32 by Peter Luschny at Mon Jun 17 08:35:19 EDT 2024

STATUS

proposed

reviewed

#31 by Jianing Song at Mon Jun 17 08:10:34 EDT 2024

STATUS

editing

proposed

#30 by Jianing Song at Mon Jun 17 08:08:28 EDT 2024

CROSSREFS