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

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

Author

Christian N. K. Anderson and Kevin L. Schwartz, Jun 04 2013

Keywords

• nonn
• base

Examples

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

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..500
• Christian N. K. Anderson, Decomposition of a(n) into its square root, and truncated cube root for n=0..500.

Crossrefs

Cf. A024770, A225873, A225885.

Programs

Mathematica

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

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

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