OFFSET
1,1
COMMENTS
Discriminant = -3360. See A139643 for more information.
The primes are congruent to {1, 121, 169, 289, 361, 529} (mod 840).
Also, primes that in 1969 were unverified values for n for the Erdos-Straus conjecture (that 4/n = 1/x + 1/y + 1/z is always solvable in natural numbers), see Mordell 1969. - Ron Knott, Dec 11 2013
There are 273 terms < 100000 in this sequence. Of these, 59 are of the form 11n-3 or 11n-4. Since 4/(11*n-3)= 1/(3*n) + 1/(3*(11*n-3)) + 1/(n*(11*n-3)) and 4/(11*n-4)= 1/(3*n-1) + 1/(3*(11*n-4)) + 1/(3*(3*n-1)*(11*n-4)), these terms can be removed from the set of primes not proved for the Erdős-Straus conjecture. For example: 1009 = 11*92-3 so 4/1009 = 1/(3*92)+1/(3*1009)+1/(92*1009). These formulas were taken from the tables in Chapter 1 of the Mishima link. - Gary Detlefs, Jan 27 2014
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section D11.
L. J. Mordell, Diophantine Equations, Academic press, 1969, pages 287-290.
LINKS
Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi).
Ron Knott, Egyptian Fractions.
H. H. Mishima, Overview of "Mathematician's Secret Room".
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references).
FORMULA
From Gary Detlefs, Jan 22 2014: (Start)
a(n) == {1,25,49,73} (mod 96);
a(n)^2 == {1,49} (mod 96);
a(n)^4 == 1 (mod 96). (End)
a(n) == {1,9,25} (mod 56). - Gary Detlefs, Jan 27 2014
MATHEMATICA
PROG
(Magma) [ p: p in PrimesUpTo(15000) | p mod 840 in {1, 121, 169, 289, 361, 529}]; // Vincenzo Librandi, Jul 29 2012
(Magma) k:=840; [p: p in PrimesUpTo(16000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, Apr 29 2008
STATUS
approved