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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.

%I A085315 #14 Oct 22 2021 22:14:30
%S A085315 1,2,7,11,101,111,1001,1011,1101,10001,10011,10101,11001,11011,100001,
%T A085315 100011,100101,100111,101001,101011,101101,110001,110011,110101,
%U A085315 111001,1000001,1000011,1000101,1000111,1001001,1001011,1001101,1010001,1010011,1011001,1100001,1100011,1100101,1101001,1110001
%N 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.
%F A085315 Solutions to rev[x^3]=rev[x]^3 without numbers divisible by 10.
%F A085315 { A069494 } minus { A008592 }. - _Alois P. Heinz_, Oct 22 2021
%e A085315 n=100111,rev[n]=111001, n^3=1003333697667631.
%e A085315 rev[n^3]=111001^3=1367667963333001=rev[n]^3.
%p A085315 r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
%p A085315 q:= n-> irem(n, 10)>0 and r(n^3)=r(n)^3:
%p A085315 select(q, [$1..2000000])[];  # _Alois P. Heinz_, Oct 22 2021
%t A085315 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
%Y A085315 Cf. A000578, A004086, A008592, A069494, A085305.
%K A085315 nonn,base
%O A085315 1,2
%A A085315 _Labos Elemer_, Jul 01 2003