login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323272 Numbers of the form p_1*p_2*p_3*...*p_r where r is 2 or an odd number > 2, and the p_i are distinct primes congruent to 1 mod 4 such that Legendre(p_i/p_j) = -1 for all i != j. 4

%I #12 Jan 12 2019 02:31:40

%S 65,85,185,265,365,481,485,493,533,565,629,685,697,785,865,949,965,

%T 985,1037,1073,1157,1165,1189,1241,1261,1285,1385,1417,1465,1565,1585,

%U 1649,1685,1765,1769,1781,1853,1865,1921,1937,1985,2117,2165,2173

%N Numbers of the form p_1*p_2*p_3*...*p_r where r is 2 or an odd number > 2, and the p_i are distinct primes congruent to 1 mod 4 such that Legendre(p_i/p_j) = -1 for all i != j.

%C If k is a term, the Pell equation x^2 - k*y^2 = -1 has a solution [Dirichlet, Newman (1977)]. This is only a sufficient condition, there are many other solutions, see A031396.

%H Chai Wah Wu, <a href="/A323272/b323272.txt">Table of n, a(n) for n = 1..10000</a>

%H Morris Newman, <a href="https://www.jstor.org/stable/2319968">A note on an equation related to the Pell equation</a>, The American Mathematical Monthly 84.5 (1977): 365-366.

%Y Cf. A002144, A031396. Includes the union of A322781 and A323271.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jan 11 2019

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)