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A319441 Cubes of non-palindromic numbers.

%I A319441 #36 Jan 05 2025 19:51:41
%S A319441 1000,1728,2197,2744,3375,4096,4913,5832,6859,8000,9261,12167,13824,
%T A319441 15625,17576,19683,21952,24389,27000,29791,32768,39304,42875,46656,
%U A319441 50653,54872,59319,64000,68921,74088,79507,91125,97336,103823,110592,117649,125000,132651,140608
%N A319441 Cubes of non-palindromic numbers.
%C A319441 This is not a subsequence of A029742. - _Bruno Berselli_, Sep 19 2018
%H A319441 Seiichi Manyama, <a href="/A319441/b319441.txt">Table of n, a(n) for n = 1..10000</a>
%H A319441 G. J. Simmons, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/8-5/elementary8-5.pdf">Palindrome cubes: Problem B-183</a>, Fibonacci Quart. 8 (1970), no. 5, p. 551.
%F A319441 a(n) = A029742(n)^3.
%e A319441 2201^3 = 10662526601 is a term.
%t A319441 palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; DeleteCases[Range[10, 110], _?palQ]^3 (* _Vincenzo Librandi_, Sep 19 2018 *)
%t A319441 Select[Range[100],!PalindromeQ[#]&]^3 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 13 2019 *)
%o A319441 (Magma) [n^3: n in [0..65] | Intseq(n) ne Reverse(Intseq(n))]; // _Vincenzo Librandi_, Sep 19 2018
%o A319441 (PARI) is_a029742(n)=my(d=digits(n)); d!=Vecrev(d) \\ after _Charles R Greathouse IV_ in A029742
%o A319441 terms(n) = my(i=0, x=1); while(1, if(i==n, break, if(is_a029742(x), print1(x^3, ", "); i++)); x++)
%o A319441 /* Print initial 40 terms as follows */
%o A319441 terms(40) \\ _Felix Fröhlich_, Sep 19 2018
%o A319441 (Python)
%o A319441 def A319441(n):
%o A319441     def f(x): return n+x//10**((l:=len(s:=str(x)))-(k:=l+1>>1))-(int(s[k-1::-1])>x%10**k)+10**(k-1+(l&1^1))-1
%o A319441     m, k = n, f(n)
%o A319441     while m != k:
%o A319441         m, k = k, f(k)
%o A319441     return m**3 # _Chai Wah Wu_, Jul 24 2024
%Y A319441 Cf. A000578, A002113, A029742, A319389, A319440.
%K A319441 nonn,base
%O A319441 1,1
%A A319441 _Seiichi Manyama_, Sep 19 2018