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A226354 Squares that become cubes when their rightmost digit is removed. 4


%S 1,4,9,16,81,10000,640000,7290000,40960000,156250000,188210961,

%T 466560000,1176490000,2621440000,5314410000,10000000000,17715610000,

%U 29859840000,48268090000,75295360000,113906250000,167772160000,241375690000,340122240000,470458810000

%N Squares that become cubes when their rightmost digit is removed.

%H Christian N. K. Anderson, <a href="/A226354/b226354.txt">Table of n, a(n) for n = 1..500</a>

%H 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 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 188210961=13719^2, while 18821096=266^3.

%t cQ[n_]:=IntegerQ[Surd[FromDigits[Most[IntegerDigits[n]]],3]]; Select[Range[ 700000]^2,cQ] (* _Harvey P. Dale_, Feb 21 2014 *)

%o (R) trimR=function(x) { x=as.character(x); ifelse(nchar(x)<2,0,substr(x,1,nchar(x)-1)) }

%o iscube<-function(x) ifelse(as.bigz(x)<2,T,all(table(as.numeric(factorize(x)))%%3==0))

%o which(sapply(1:6400,function(x) iscube(trimR(x^2))))^2

%Y Cf. A024770, A225873, A225885.

%K nonn,base

%O 1,2

%A _Christian N. K. Anderson_ and _Kevin L. Schwartz_, Jun 04 2013

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Last modified June 17 06:06 EDT 2019. Contains 324183 sequences. (Running on oeis4.)