A085315 Numbers such that first reversing digits and after forming its cube equals the result of first-form-cube and after-reverse operation with exclusion of cases divisible by 10.

1, 2, 7, 11, 101, 111, 1001, 1011, 1101, 10001, 10011, 10101, 11001, 11011, 100001, 100011, 100101, 100111, 101001, 101011, 101101, 110001, 110011, 110101, 111001, 1000001, 1000011, 1000101, 1000111, 1001001, 1001011, 1001101, 1010001, 1010011, 1011001, 1100001, 1100011, 1100101, 1101001, 1110001

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Formula

Solutions to rev[x^3]=rev[x]^3 without numbers divisible by 10.

{ A069494 } minus { A008592 }. - Alois P. Heinz, Oct 22 2021

Example

n=100111,rev[n]=111001, n^3=1003333697667631.
rev[n^3]=111001^3=1367667963333001=rev[n]^3.

Maple

r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
q:= n-> irem(n, 10)>0 and r(n^3)=r(n)^3:
select(q, [$1..2000000])[];  # Alois P. Heinz, Oct 22 2021

Mathematica

nd[x_, y_] := 10*x+y; tn[x_] := Fold[nd, 0, x] rt[x_] := tn[Reverse[IntegerDigits[x]]] Do[s=rt[n^3]; s1=rt[n]^3; If[Equal[s, s1]&& !Equal[Mod[n, 10], 0], k=k+1; Print[n]], {n, 1, 10000000}]; k

Crossrefs

Cf. A000578, A004086, A008592, A069494, A085305.

Sequence in context: A101592 A349709 A135066 * A002780 A069885 A069748

Adjacent sequences: A085312 A085313 A085314 * A085316 A085317 A085318

Keyword

nonn,base

Author

Labos Elemer, Jul 01 2003

Status

approved