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A112860
2 together with A053032.
21
2, 11, 19, 29, 31, 59, 71, 79, 101, 131, 139, 151, 179, 181, 191, 199, 211, 229, 239, 251, 271, 311, 331, 349, 359, 379, 419, 431, 439, 461, 479, 491, 499, 509, 521, 541, 571, 599, 619, 631, 659, 691, 709, 719, 739, 751, 809, 811, 839, 859, 911, 919, 941, 971
OFFSET
1,1
COMMENTS
Consists of the primes that are in neither A053027 nor A053028.
From Jianing Song, Jun 16 2024: (Start)
Primes p such that A001176(p) = 1.
For p > 2, p is in this sequence if and only if A001175(p) == 2 (mod 4), and if and only if A001177(p) == 2 (mod 4). For a proof of the equivalence between A001176(p) = 1 and A001177(p) == 2 (mod 4), see Section 2 of my link below.
This sequence contains all primes congruent to 11, 19 (mod 20). This corresponds to case (3) 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]
LINKS
C. Ballot and M. Elia, Rank and period of primes in the Fibonacci sequence; a trichotomy, Fib. Quart., 45 (No. 1, 2007), 56-63 (The sequence B1).
CROSSREFS
Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n+2) = m*x(n+1) + x(n). Let w(k) be the number of zeros in a fundamental period of {x(n)} modulo k.
| m=1 | m=2 | m=3
-----------------------------+-----------+---------+---------
The sequence {x(n)} | A000045 | A000129 | A006190
The sequence {w(k)} | A001176 | A214027 | A322906
Primes p such that w(p) = 1 | this seq* | A309580 | A309586
Primes p such that w(p) = 2 | A053027 | A309581 | A309587
Primes p such that w(p) = 4 | A053028 | A261580 | A309588
Numbers k such that w(k) = 1 | A053031 | A309583 | A309591
Numbers k such that w(k) = 2 | A053030 | A309584 | A309592
Numbers k such that w(k) = 4 | A053029 | A309585 | A309593
* and also A053032 U {2}
Sequence in context: A117196 A304811 A064739 * A152312 A154765 A163997
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 30 2007
STATUS
approved