cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A050802 Squares expressible as the sum of two positive cubes in at least one way.

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%I A050802 #30 Jan 08 2019 09:12:41
%S A050802 9,16,576,1024,6561,9604,11664,28224,36864,51984,65536,97344,140625,
%T A050802 250000,275625,345744,419904,450241,614656,717409,746496,1028196,
%U A050802 1058841,1399489,1500625,1590121,1750329,1806336,1882384,2359296
%N A050802 Squares expressible as the sum of two positive cubes in at least one way.
%D A050802 "Game, Set and Math" by Ian Stewart, Chapter 8 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
%H A050802 Tony D. Noe and Harry J. Smith, <a href="/A050802/b050802.txt">Table of n, a(n) for n = 1..1000</a>
%H A050802 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A050802 a(n) = A050801(n)^2. - _Jonathan Sondow_, Oct 28 2013
%e A050802 E.g., 717409 = 847^2 = 33^3 + 88^3.
%e A050802 169 = 13^2 = (-7)^3 + 8^3 is not a member, because 169 is not the sum of two positive cubes. - _Jonathan Sondow_, Oct 28 2013
%t A050802 ok[n_] := Length[Select[PowersRepresentations[n, 2, 3], #[[1]] != 0 & ]] >= 1; Select[Range[1600]^2, ok]
%t A050802 (* _Jean-François Alcover_, Apr 22 2011 *)
%t A050802 Union[Select[Total/@Tuples[Range[250]^3,2],IntegerQ[Sqrt[#]]&]] (* _Harvey P. Dale_, Mar 04 2012 *)
%o A050802 (PARI) { nstart=1; a2start=9; n=nstart; a=sqrtint(a2start)-1; until (0, a=a+1; a2=a*a; b1=((a2/2)^(1/3))\1; for (b=b1, a, b3=b*b*b; c1=1; if (a2 > b3, c1=((a2-b3)^(1/3))\1;); for (c=c1, b, d=b3 + c*c*c; if (d > a2 && c == 1, break(2)); if (d > a2, break); if (a2 == d, print(n, " ", a2); write("b050802.txt", n, " ", a2); n=n+1; break(2); ); ) ) ) } \\ _Harry J. Smith_, Jan 15 2009
%o A050802 (PARI) is(n)=for(k=sqrtnint((n+1)\2,3),sqrtnint(n-1,3),if(ispower(n-k^3,3),return(issquare(n))));0 \\ _Charles R Greathouse IV_, Oct 28 2013
%Y A050802 Cf. A038597, A050801, A050803, A106265, A217248.
%K A050802 nonn,nice,easy
%O A050802 1,1
%A A050802 _Patrick De Geest_, Sep 15 1999
%E A050802 More terms from _Michel ten Voorde_
%E A050802 Definition corrected by _Jonathan Sondow_, Oct 28 2013