|
Search: id:A097056
|
|
|
| A097056 |
|
Numbers n such that the interval n^2 < x < (n+1)^2 contains two or more distinct non-square perfect powers A097054. |
|
+0
3
|
|
| 5, 11, 46, 2536, 558640, 572783, 3362407, 7928108, 8928803, 67460050, 106938971, 1763350849, 2501641555, 2756149047, 4584349318, 5713606932, 17941228664, 375376083513, 411124334926, 452894760105, 1167680330892, 1933159894790, 1946131548918, 2506032014606, 2507269866902, 8217688694093
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Empirically, there seem to be no intervals between consecutive squares containing more than two non-square perfect powers. a(5)..a(20) from Don Reble (djr(AT)nk.ca).
|
|
EXAMPLE
|
a(1)=5: 5^2<3^3<2^5<6^2, a(2)=11: 11^2<5^3<2^7<12^2, a(4)=2536: 2536^2<x<2537^2 (6431296,6436369) contains 23^5=6436343 and 186^3=6434856.
22 is not in the sequence because 2^9 and 8^3 (22^2<512<23^2) are not distinct.
|
|
CROSSREFS
|
Cf. A000290 the squares, A097054 non-square perfect powers, A097055 intervals between consecutive squares containing non-square perfect powers.
Sequence in context: A055113 A129015 A141355 this_sequence A092358 A079029 A106953
Adjacent sequences: A097053 A097054 A097055 this_sequence A097057 A097058 A097059
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 21 2004
|
|
EXTENSIONS
|
More terms from David Wasserman (dwasserm(AT)earthlink.net), Dec 17 2007
|
|
|
Search completed in 0.002 seconds
|
