login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A097934 Primes p such that p divides 3^((p-1)/2) - 2^((p-1)/2). 5
5, 19, 23, 29, 43, 47, 53, 67, 71, 73, 97, 101, 139, 149, 163, 167, 173, 191, 193, 197, 211, 239, 241, 263, 269, 283, 293, 307, 311, 313, 317, 331, 337, 359, 379, 383, 389, 409, 431, 433, 457, 461, 479, 499, 503, 509, 523, 547, 557, 571, 577, 599, 601, 619 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Rational primes that decompose in the field Q(sqrt(6)). - N. J. A. Sloane, Dec 26 2017

Set x=3,d=1,s=-1 in pari program.

All terms belong to A038876(n) = Primes p such that 6 is a square mod p. Only first two terms of A038876(n), 2 and 3, do not belong to a(n). - Alexander Adamchuk, May 04 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

FORMULA

a(n) = A038876(n+1). - Alexander Adamchuk, May 04 2007

EXAMPLE

For p=5, 3^2 - 2^2 = 5.

MATHEMATICA

okQ[n_]:=Module[{c=(n-1)/2}, Divisible[3^c-2^c, n]];  Select[Prime[Range[200]], okQ]  (* Harvey P. Dale, Apr 13 2011 *)

PROG

(PARI) \s = +-1, d=diff ptopm1d2(n, x, d, s) = { forprime(p=3, n, p2=(p-1)/2; y=x^p2 + s*(x-d)^p2; if(y%p==0, print1(p", "))) }

CROSSREFS

Cf. A038876 = Primes p such that 6 is a square mod p.

Sequence in context: A074229 A152912 A191054 * A191609 A191084 A146509

Adjacent sequences:  A097931 A097932 A097933 * A097935 A097936 A097937

KEYWORD

nonn

AUTHOR

Cino Hilliard, Sep 04 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 16:00 EST 2020. Contains 331961 sequences. (Running on oeis4.)