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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A092572 Numbers of the form x^2 + 3y^2 where x and y are positive integers. 34
 4, 7, 12, 13, 16, 19, 21, 28, 31, 36, 37, 39, 43, 48, 49, 52, 57, 61, 63, 64, 67, 73, 76, 79, 84, 91, 93, 97, 100, 103, 108, 109, 111, 112, 117, 124, 127, 129, 133, 139, 144, 147, 148, 151, 156, 157, 163, 169, 171, 172, 175, 181, 183, 189, 192, 193, 196, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Superset of primes of the form 6n+1 (A002476). It seems that all integer solutions of ((a+b)^3 - (a-b)^3) / (2*b) = c^3 have c = x^2 + 3*y^2. - Juergen Buchmueller (pullmoll(AT)t-online.de), Apr 04 2008 To prove the case of cubes in Fermat's last theorem, Euler considered numbers of the form a^2 + 3b^2. In the equation x^3 + y^3 = z^3, Euler specified that x = a - b and y = a + b. - Alonso del Arte, Jul 19 2012 All terms == 0,1,3,4, or 7 (mod 9). - Robert Israel, Apr 03 2017 REFERENCES Paulo Ribenboim, 13 Lectures on Fermat's Last Theorem. New York: Springer-Verlag (1979): 4. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 E. Akhtarkavan, M. F. M. Salleh and O. Sidek, Multiple Descriptions Video Coding Using Coinciding Lattice Vector Quantizer for H.264/AVC and Motion JPEG2000, World Applied Sciences Journal 21 (2): 157-169, 2013. - From N. J. A. Sloane, Feb 11 2013 Eric Weisstein's World of Mathematics, Eulers 6n Plus 1 Theorem EXAMPLE 7 is of the specified form, since 2^2 + 3 * 1^2 = 7. So is 12, since 3^2 + 3 * 1^2 = 12, and 13, with 1^2 + 3 * 2^2 = 13. MAPLE N:= 1000: # to get all terms <= N S:= {seq(seq(x^2 + 3*y^2, x = 1 .. floor(sqrt(N - 3*y^2))),   y=1..floor(sqrt(N/3-1)))}: sort(convert(S, list)); # Robert Israel, Apr 03 2017 MATHEMATICA Union[Flatten[Table[a^2 + 3b^2, {a, 20}, {b, Ceiling[Sqrt[(400 - a^2)/3]]}]]] (* Alonso del Arte, Jul 19 2012 *) CROSSREFS Cf. A002476, A092573, A092575, A158937 (similar definition but with duplicates left in). Sequence in context: A249918 A340244 A158937 * A092574 A310769 A058271 Adjacent sequences:  A092569 A092570 A092571 * A092573 A092574 A092575 KEYWORD nonn AUTHOR Eric W. Weisstein, Feb 28 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.

Last modified May 9 19:07 EDT 2021. Contains 343746 sequences. (Running on oeis4.)