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

Author

Labos Elemer, Jul 01 2003

Keywords

• nonn
• base

Examples

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

Crossrefs

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

Programs

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

Formula

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

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