|
Search: id:A062717
|
|
|
| A062717 |
|
Numbers n such that 6n+1 is a perfect square. |
|
+0
12
|
|
| 0, 4, 8, 20, 28, 48, 60, 88, 104, 140, 160, 204, 228, 280, 308, 368, 400, 468, 504, 580, 620, 704, 748, 840, 888, 988, 1040, 1148, 1204, 1320, 1380, 1504, 1568, 1700, 1768, 1908, 1980, 2128, 2204, 2360, 2440, 2604, 2688, 2860, 2948, 3128, 3220, 3408, 3504
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Sequence allows us to find X values of the equation: 6*X^3 + X^2 = Y^2. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
Averages of the Triangular numbers which take integer values. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
FORMULA
|
G.f.: (4x^3+4x^2+4x)/[(1-x)(1-x^2)^2].
a(2n)=n(6n+2), a(2n+1)=6*n^2+10n+4. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
|
|
MATHEMATICA
|
a=b=0; lst={}; Do[b=(a+=n*(n-1)/2)/n; If[b==IntegerPart[b], AppendTo[lst, b]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
|
|
PROGRAM
|
(PARI) je=[]; for(n=0, 7000, if(issquare(6*n+1), je=concat(je, n))); je
(PARI) { n=0; for (m=0, 10^9, if (issquare(6*m + 1), write("b062717.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 09 2009]
|
|
CROSSREFS
|
Equals 4 * A001318.
Cf. A005563, A046092, A001082, A002378, A036666.
Cf. A160757, A000217 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
Adjacent sequences: A062714 A062715 A062716 this_sequence A062718 A062719 A062720
Sequence in context: A061814 A087254 A160726 this_sequence A084922 A047185 A034733
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jason Earls (zevi_35711(AT)yahoo.com), Jul 14 2001
|
|
|
Search completed in 0.002 seconds
|
