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 A087285 Possible differences between a cube and the next smaller square. 10
 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 See under A081121. 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 Cf. A087286, A088017, A081121, A077116, A065733. Sequence in context: A240106 A206853 A229618 * A107791 A181518 A262231 Adjacent sequences:  A087282 A087283 A087284 * A087286 A087287 A087288 KEYWORD nonn AUTHOR Hugo Pfoertner, Sep 18 2003 STATUS approved

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