cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A154755 Primes p such that ratio in A154754 is 1.

Original entry on oeis.org

2, 3, 5, 11, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 83, 89, 97, 101, 107, 113, 131, 137, 149, 157, 167, 173, 179, 181, 191, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331, 347, 353, 359, 367, 379, 383, 389, 397
Offset: 1

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Author

T. D. Noe, Jan 15 2009

Keywords

Comments

All primes of the form 6k-1 are in this sequence. In addition, about half of all primes of the form 6k+1 appear to be here. See A154756 for the primes not in this sequence.

Crossrefs

A000073

A154756 Primes p such that ratio in A154754 is 3.

Original entry on oeis.org

7, 13, 19, 61, 73, 79, 103, 109, 127, 139, 151, 163, 193, 199, 211, 241, 271, 307, 337, 349, 373, 409, 421, 523, 541, 547, 571, 607, 613, 673, 739, 757, 769, 787, 811, 853, 877, 883, 907, 919, 937, 967, 991, 1009, 1033, 1063, 1087, 1117, 1123, 1129, 1201
Offset: 1

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Author

T. D. Noe, Jan 15 2009

Keywords

Comments

Note that all these primes have the form 6k+1, which is required for the equation x^2+x+1=0 (mod p) to have two integer solutions. However, this sequence has only about half of all 6k+1 primes. What other condition determines the p in this sequence? See A154755 for the primes not in this sequence.

Crossrefs

Cf. A000073

A386236 Ratio of the period and the reduced period of the Fibonacci 3-step sequence A000073 mod n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 3, 3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 3, 1, 3, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 1, 3, 1, 3, 3, 1, 1, 3, 3, 3, 3, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 3, 3, 3
Offset: 1

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Author

Peter Munn, Jul 16 2025

Keywords

Comments

The period is A046738(n) and the reduced period is A046737(n).
See also the information in A154754 and A046737.

Links

Crossrefs

Cf. A000073, A046737, A046738.
The equivalent sequence for Fibonacci numbers is A001176.
Cf. A060839 (differs first at n=31), A154754 (restriction to prime indices).

Formula

a(n) = A046738(n)/A046737(n).

A154753 Reduced period of the Fibonacci 3-step sequence A000073 mod prime(n).

Original entry on oeis.org

4, 13, 31, 16, 110, 56, 96, 120, 553, 140, 331, 469, 560, 308, 46, 52, 3541, 620, 1519, 5113, 1776, 1040, 287, 8011, 3169, 680, 17, 1272, 330, 12883, 1792, 5720, 18907, 1288, 7400, 950, 8269, 54, 9296, 2494, 32221, 10981, 36673, 1552, 3234, 66, 1855
Offset: 1

Views

Author

T. D. Noe, Jan 15 2009

Keywords

Comments

The Fibonacci 3-step (tribonacci) sequence t(k) begins (with offset -2) 1,0,0. For a prime p, the reduced period r is the least number such that p divides both t(r-1) and t(r); i.e., "0,0" appears in the sequence mod p. The ratio of the period A106302 and the reduced period is either 1 or 3; see A154754.

Examples

			The tribonacci sequence (starting with 1) mod 7 begins with the 48 terms 1,1,2,4,0,6,3,2,4,2,1,0,3,4,0,0,4,4,1,2,0,3,5,1,2,1,4,0,5,2,0,0,2,2,4,1, 0,5,6,4,1,4,2,0,6,1,0,0. The first "0,0" terms occur at index 16. Hence a(4)=16.

Links

Crossrefs

Cf. A046737, A046738.

Formula

a(n) = A046738(prime(n)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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