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.

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A106274 Numbers k for which the absolute value of the discriminant of the polynomial x^k - x^(k-1) - ... - x - 1 is prime.

Original entry on oeis.org

2, 4, 6, 26, 158
Offset: 1

Views

Author

T. D. Noe, May 02 2005

Keywords

Comments

This polynomial is the characteristic polynomial of the Fibonacci and Lucas k-step recursions. Are the k-step recursions different -- in some way -- for the values of k that yield a prime discriminant? No other k < 10000.

Links

Crossrefs

Cf. A106273 (discriminant of the polynomial x^n - x^(n-1) - ... - x - 1).

A106275 Numbers k for which the absolute value of the discriminant of the polynomial x^k - x^(k-1) - ... - x - 1 is a prime times 2^m for some m >= 0.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 21, 26, 99, 158, 405
Offset: 1

Views

Author

T. D. Noe, May 02 2005

Keywords

Comments

This polynomial is the characteristic polynomial of the Fibonacci and Lucas k-step recursions. Are the k-step recursions different -- in some way -- for the values of k that yield a prime*2^m discriminant? No other k < 10000.

Links

Crossrefs

Cf. A106273 (discriminant of the polynomial x^n - x^(n-1) - ... - x - 1).

Programs

  • PARI
    f(n) = poldisc('x^n-sum(k=0, n-1, 'x^k)); \\ A106273
isok(k) = my(x=abs(f(k))); ispseudoprime(x) || ispseudoprime(x/2^valuation(x, 2)); \\ Michel Marcus, Mar 26 2024

A106292 Period of the Lucas sequence A000032 mod prime(n).

Original entry on oeis.org

3, 8, 4, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178, 90, 190, 388, 396, 22, 42, 448, 456, 114, 52, 238, 240, 250, 516, 176, 268, 270, 556, 56
Offset: 1

Views

Author

T. D. Noe, May 02 2005

Keywords

Comments

This sequence differs from A060305 at only one position: 3, which corresponds to the prime 5, which is the discriminant of the characteristic polynomial x^2-x-1. We have a(n) < prime(n) for the primes in A038872.

Links

Crossrefs

Cf. A060305 (period of Fibonacci numbers mod prime(n)), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106291.

Programs

  • Mathematica
    n=2; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 70}]

Formula

a(n) = A106291(prime(n)).
Previous Showing 11-13 of 13 results.

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

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