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

1,2

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.

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

Cf. A024770, A225873, A225885.

Sequence in context: A038239 A352919 A263094 * A299921 A089149 A082920

Adjacent sequences: A226351 A226352 A226353 * A226355 A226356 A226357

Keyword

nonn,base

Author

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

Status

approved