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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.
3
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
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
KEYWORD
nonn,base
AUTHOR
Labos Elemer, Jul 01 2003
STATUS
approved