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%I #15 Oct 07 2013 13:24:42
%S 2,4,7,11,13,15,19,20,26,28,35,39,40,45,47,48,49,53,55,56,60,63,67,74,
%T 76,79,81,83,100,104,107,109,116,127,135,139,146,147,148,150,152,155,
%U 170,174,180,184,186,191,193,200,207,212,215,216,233,235,242,244,249
%N Possible differences between a cube and the next smaller square.
%C Sequence and program were provided by _Ralf Stephan_ Aug 28 2003.
%C 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.
%C 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
%D See under A081121.
%e a(1)=2 because the next smaller square below 3^3=27 is 5^2=25.
%o (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",")))
%Y Cf. A087286, A088017, A081121, A077116, A065733.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Sep 18 2003
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