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.

A234787 Cubes (with at least two digits) that become squares when their rightmost digit is removed.

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%I A234787 #27 Dec 15 2019 08:36:07
%S A234787 1000,64000,729000,4096000,15625000,46656000,117649000,262144000,
%T A234787 531441000,1000000000,1771561000,2985984000,4826809000,7529536000,
%U A234787 11390625000,16777216000,24137569000,34012224000,47045881000,64000000000
%N A234787 Cubes (with at least two digits) that become squares when their rightmost digit is removed.
%C A234787 With the help of the Nagell-Lutz theorem it is easy to prove that there are no other solutions than those of the form 1000*n^6.
%H A234787 Georg Fischer, <a href="/A234787/b234787.txt">Table of n, a(n) for n = 1..300</a> [a(1..204) from Reiner Moewald]
%H A234787 Wikipedia, <a href="https://en.wikipedia.org/wiki/Nagell%E2%80%93Lutz_theorem">Nagell-Lutz theorem</a>.
%H A234787 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A234787 a(n) = 1000*n^6.
%F A234787 From _Colin Barker_, Dec 15 2019: (Start)
%F A234787 G.f.: 1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7.
%F A234787 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A234787 (End)
%o A234787 (PARI) lista(nn) = {for (n=1, nn, if (((cb = n^3) > 10) && issquare(cb\10), print1(cb, ", ")););} \\ _Michel Marcus_, Jan 10 2014
%o A234787 (PARI) Vec(1000*x*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^40)) \\ _Colin Barker_, Dec 15 2019
%Y A234787 Cf. A226354.
%Y A234787 Subsequence of A000578.
%K A234787 nonn,base,easy
%O A234787 1,1
%A A234787 _Reiner Moewald_, Dec 30 2013