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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 (list; graph; refs; listen; history; text; internal format)
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: A038784 A038239 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

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Last modified May 24 17:16 EDT 2019. Contains 323533 sequences. (Running on oeis4.)