|
Search: id:A080761
|
|
|
| A080761 |
|
Conjectured list of positive numbers of the form y^2 - x^3, x and y >= 1. |
|
+0
5
|
|
| 1, 3, 8, 9, 12, 15, 17, 18, 19, 22, 24, 28, 30, 35, 36, 37, 38, 40, 41, 44, 48, 54, 55, 56, 57, 63, 64, 65, 68, 71, 73, 79, 80, 89, 92, 94, 97, 98, 99, 100, 101, 105, 106, 107, 108, 112, 113, 117, 119, 120, 121, 128, 129, 131, 132, 136, 138, 141, 142, 143, 145, 148, 151
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Obtained by considering only values of x <= 10^6.
Comments from Artur Jasinski (grafix(AT)csl.pl), Oct 03 2007 (Start): Some numbers have multiple partitions:
8 = 4^2 - 8^3 = 312^2 - 46^39
9 = 6^2 - 3^3 = 15^2 - 6 ^3 = 253^2 - 40^2
17 = 5^2 - 2^3 = 9^2 - 4^3 = 23^2 - 8^3 = 282^2 - 43^3 = 365^2 - 52^2 = 378661^2-5234^3 (First squared factor: A029727, Second cubed factor: A029728)
24 = 32^2 - 10^2 = 736844^2 - 8158^3
36 = 10^2 - 4^3 = 42^2 - 12^3
57 = 11^2 - 4^3 = 20^2 - 7^3
65 = 53^2 - 14^3 = 14113^2 - 584^3
73 = 17^2 - 6^3 = 611^2 - 72^3 = 6717^2 - 365^3
89 = 33^2 - 10^3 = 408^2 - 55^3
100 = 90^2 - 20^3 = 118^2 - 24^3 = 137190^2 - 2660^3
108 = 18^2 - 6^3 = 7002^2 - 366^3
113 = 25^2 - 8^3 = 38^2 - 11^3 = 133^2 - 26^3 = 8669^2 - 422^3 (First squared factor: A134042 Second cubed factor: A134043
141 = 22^2 - 7^3 = 169852^2 - 3067^3
|
|
LINKS
|
Cino Hilliard, Proof that n^3+7 <> k^2 for all integers n,k.
|
|
EXAMPLE
|
8 is in the sequence since 3^2 = 1^3 + 8.
|
|
PROGRAM
|
(PARI) diop(n, m) = { for(p=1, m, for(x=1, n, y=x*x*x+p; if(issquare(y), print1(p" "); break) ) ) }
|
|
CROSSREFS
|
Complement of A080762.
Cf. sequences for n^3+7, n^3+17, n^3+3, n^3+2, n^3+5.
Cf. A029727, A029728, A134042, A134043.
Sequence in context: A028960 A139491 A084387 this_sequence A087286 A165289 A066494
Adjacent sequences: A080758 A080759 A080760 this_sequence A080762 A080763 A080764
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Mar 10 2003
|
|
EXTENSIONS
|
"Positive" added to definition by N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2007
|
|
|
Search completed in 0.002 seconds
|
