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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

Table of n, a(n) for n=1..59.

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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Last modified August 20 13:04 EDT 2017. Contains 290835 sequences.