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.

A226354 Squares that become cubes when their rightmost digit is removed.

This page as a plain text file.
%I A226354 #32 Feb 15 2018 16:25:35
%S A226354 1,4,9,16,81,10000,640000,7290000,40960000,156250000,188210961,
%T A226354 466560000,1176490000,2621440000,5314410000,10000000000,17715610000,
%U A226354 29859840000,48268090000,75295360000,113906250000,167772160000,241375690000,340122240000,470458810000
%N A226354 Squares that become cubes when their rightmost digit is removed.
%H A226354 Christian N. K. Anderson, <a href="/A226354/b226354.txt">Table of n, a(n) for n = 1..500</a>
%H A226354 Christian N. K. Anderson, <a href="/A226354/a226354.txt">Decomposition of a(n) into its square root, and truncated cube root</a> for n=0..500.
%F A226354 For n > 11: a(n)=(100*(n-6)^3)^2 (188210961 is the last "exception" as is easy to prove with the help of the Nagell-Lutz theorem). - _Reiner Moewald_, Dec 30 2013
%e A226354 188210961=13719^2, while 18821096=266^3.
%t A226354 cQ[n_]:=IntegerQ[Surd[FromDigits[Most[IntegerDigits[n]]],3]]; Select[Range[ 700000]^2,cQ] (* _Harvey P. Dale_, Feb 21 2014 *)
%o A226354 (R) trimR=function(x) { x=as.character(x); ifelse(nchar(x)<2,0,substr(x,1,nchar(x)-1)) }
%o A226354 iscube<-function(x) ifelse(as.bigz(x)<2,T,all(table(as.numeric(factorize(x)))%%3==0))
%o A226354 which(sapply(1:6400,function(x) iscube(trimR(x^2))))^2
%Y A226354 Cf. A024770, A225873, A225885.
%K A226354 nonn,base
%O A226354 1,2
%A A226354 _Christian N. K. Anderson_ and _Kevin L. Schwartz_, Jun 04 2013