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.

A085606 a(n) = (n-1)^n - 1.

Original entry on oeis.org

0, -1, 0, 7, 80, 1023, 15624, 279935, 5764800, 134217727, 3486784400, 99999999999, 3138428376720, 106993205379071, 3937376385699288, 155568095557812223, 6568408355712890624, 295147905179352825855, 14063084452067724991008, 708235345355337676357631
Offset: 0

Views

Author

Lekraj Beedassy, Jul 07 2003

Keywords

Comments

Sequence relates to the "monkey and coconut problem"(A014293) giving the number of coconuts received by each of the n sailors from the ultimate equitable distribution the next day.
From Alexander Adamchuk, Nov 13 2006: (Start)
4n^2 divides a(2n).
Odd prime p divides a(p-1).
8p^2 divides a(2p) for an odd prime p.
32p^4 divides a(2p^2) for an odd prime p.
64p^8 divides a(2p^4) for an odd prime p.
p^3 divides a(p^3+2) for prime p.
p divides a((p-1)/2) for prime p in A157437.
p^2 divides a((p-1)/2) for prime p = {5,127,607}. (End)

Crossrefs

Cf. A014293, A007778, A065440, A037205, A157437.

Programs

Formula

a(n) = A065440(n) - 1.

Extensions

More terms from Ray Chandler, Nov 10 2003

A191059 Primes p that have Kronecker symbol (p|6) = -1.

Original entry on oeis.org

13, 17, 19, 23, 37, 41, 43, 47, 61, 67, 71, 89, 109, 113, 137, 139, 157, 163, 167, 181, 191, 211, 229, 233, 239, 257, 263, 277, 281, 283, 307, 311, 331, 349, 353, 359, 373, 379, 383, 397, 401, 421, 431, 449, 479, 499, 503, 521, 523, 541, 547, 569, 571, 593
Offset: 1

Views

Author

T. D. Noe, May 25 2011

Keywords

Comments

Inert rational primes in the field Q(sqrt(-6)). - N. J. A. Sloane, Dec 26 2017
Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6) = 5. - Gary Detlefs, May 26 2014
Originally erroneously named "Primes that are not squares mod 6". - M. F. Hasler, Jan 18 2016
From Jianing Song, Oct 23 2024: (Start)
Primes p such that the Legendre symbol (-6/p) = -1, i.e., -6 is not a square modulo p.
Primes congruent to {13, 17, 19, 23} module 24. (End)

Links

Crossrefs

Cf. A157437.

Programs

  • Magma
    [p: p in PrimesUpTo(593) | KroneckerSymbol(p, 6) eq -1]; // Vincenzo Librandi, Sep 11 2012
  • Mathematica
    Select[Prime[Range[200]], JacobiSymbol[#,6]==-1&]
  • PARI
    is(n)=isprime(n) && kronecker(n,6)<0 \\ Charles R Greathouse IV, Feb 23 2017

Extensions

Definition corrected, following a suggestion from David Broadhurst, by M. F. Hasler, Jan 18 2016

A296924 Primes p such that Legendre(-6,p) = 0 or 1.

Original entry on oeis.org

2, 3, 5, 7, 11, 29, 31, 53, 59, 73, 79, 83, 97, 101, 103, 107, 127, 131, 149, 151, 173, 179, 193, 197, 199, 223, 227, 241, 251, 269, 271, 293, 313, 317, 337, 347, 367, 389, 409, 419, 433, 439, 443, 457, 461, 463, 467, 487, 491, 509, 557, 563, 577, 587, 601, 607, 631, 653, 659, 673, 677, 683
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Comments

Primes == 1, 2, 3, 5, 7, or 11 (mod 24). - Robert Israel, Dec 27 2017

Links

Crossrefs

Cf. A157437, A191059.

Programs

  • Maple
    Load the Maple program HH given in A296920. Then run HH(-6, 200); This produces A157437, A191059, and the present sequence.
select(isprime, {seq(seq(24*i+j,j=[1,2,3,5,7,11]),i=0..100)});

A157438 Primes p such that p^2 divides A085606((p-1)/2) = ((p-1)/2-1)^((p-1)/2) - 1.

Original entry on oeis.org

5, 127, 607
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2009

Keywords

Comments

Primes p such that (-3/2)^((p-1)/2) == 1 - p/6 (mod p^2).[Max Alekseyev, Dec 05 2010]
Primes p that divide A085606((p-1)/2) are listed in A157437.
No other terms below 10^11. [From Max Alekseyev, Dec 05 2010.]

Crossrefs

Cf. A085606, A157437.
Showing 1-4 of 4 results.

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

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