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