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A226354
Squares that become cubes when their rightmost digit is removed.
4
1, 4, 9, 16, 81, 10000, 640000, 7290000, 40960000, 156250000, 188210961, 466560000, 1176490000, 2621440000, 5314410000, 10000000000, 17715610000, 29859840000, 48268090000, 75295360000, 113906250000, 167772160000, 241375690000, 340122240000, 470458810000
OFFSET
1,2
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..500
FORMULA
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
EXAMPLE
188210961=13719^2, while 18821096=266^3.
MATHEMATICA
cQ[n_]:=IntegerQ[Surd[FromDigits[Most[IntegerDigits[n]]], 3]]; Select[Range[ 700000]^2, cQ] (* Harvey P. Dale, Feb 21 2014 *)
PROG
(R) trimR=function(x) { x=as.character(x); ifelse(nchar(x)<2, 0, substr(x, 1, nchar(x)-1)) }
iscube<-function(x) ifelse(as.bigz(x)<2, T, all(table(as.numeric(factorize(x)))%%3==0))
which(sapply(1:6400, function(x) iscube(trimR(x^2))))^2
CROSSREFS
KEYWORD
nonn,base
STATUS
approved