|
|
A087285
|
|
Possible differences between a cube and the next smaller square.
|
|
11
|
|
|
2, 4, 7, 11, 13, 15, 19, 20, 26, 28, 35, 39, 40, 45, 47, 48, 49, 53, 55, 56, 60, 63, 67, 74, 76, 79, 81, 83, 100, 104, 107, 109, 116, 127, 135, 139, 146, 147, 148, 150, 152, 155, 170, 174, 180, 184, 186, 191, 193, 200, 207, 212, 215, 216, 233, 235, 242, 244, 249
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Sequence and program were provided by Ralf Stephan Aug 28 2003.
Comment from David W. Wilson, Jan 05 2009: I believe there is an algorithm for solving x^3 - y^2 = k, which should have a finite number of solutions for any k. That means that we should in principle be able to compute this sequence.
Up to the initial 0 in A165288, these two sequences appear to be the same, but according to its current definition, A165288 should be the same as the (different) sequence A229618 = the range of the sequence A181138 (= least k>0 such that n^2+k is a cube): If n^2+k=y^3 is the smallest cube above n^2, then n^2 is not necessarily the largest square below y^3. E.g., 18 is in A181138 and A229618, since 9+18=27 is the least cube above 9=3^2, but 25=5^2 is the largest square below 27. - M. F. Hasler, Oct 05 2013
|
|
REFERENCES
|
|
|
LINKS
|
|
|
EXAMPLE
|
a(1)=2 because the next smaller square below 3^3=27 is 5^2=25.
|
|
PROG
|
(PARI) v=vector(200):for(n=2, 10^7, t=n^3:s=sqrtint(t)^2: if(s==t, s=sqrtint(t-1)^2):tt=t-s: if(tt>0&&tt<=200&&!v[tt], v[tt]=n)):for(k=1, 200, if(v[k], print1(k", ")))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|