A087285 Possible differences between a cube and the next smaller square.

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

Offset: 1

Author

Hugo Pfoertner, Sep 18 2003

Keywords

• nonn

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

Examples

			a(1)=2 because the next smaller square below 3^3=27 is 5^2=25.
		

References

• See under A081121.

Crossrefs

Cf. A087286, A088017, A081121, A077116, A065733.

Programs

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",")))