A319441 Cubes of non-palindromic numbers.

1000, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 39304, 42875, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 91125, 97336, 103823, 110592, 117649, 125000, 132651, 140608

Offset

1,1

Comments

This is not a subsequence of A029742. - Bruno Berselli, Sep 19 2018

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

G. J. Simmons, Palindrome cubes: Problem B-183, Fibonacci Quart. 8 (1970), no. 5, p. 551.

Formula

a(n) = A029742(n)^3.

Example

2201^3 = 10662526601 is a term.

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; DeleteCases[Range[10, 110], _?palQ]^3 (* Vincenzo Librandi, Sep 19 2018 *)
Select[Range[100], !PalindromeQ[#]&]^3 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2019 *)

Prog

(Magma) [n^3: n in [0..65] | Intseq(n) ne Reverse(Intseq(n))]; // Vincenzo Librandi, Sep 19 2018
(PARI) is_a029742(n)=my(d=digits(n)); d!=Vecrev(d) \\ after Charles R Greathouse IV in A029742
terms(n) = my(i=0, x=1); while(1, if(i==n, break, if(is_a029742(x), print1(x^3, ", "); i++)); x++)
/* Print initial 40 terms as follows */
terms(40) \\ Felix Fröhlich, Sep 19 2018
(Python)
def A319441(n):
    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
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m**3 # Chai Wah Wu, Jul 24 2024

Crossrefs

Cf. A000578, A002113, A029742, A319389, A319440.

Sequence in context: A004265 A004266 A004267 * A202456 A168650 A043491

Adjacent sequences: A319438 A319439 A319440 * A319442 A319443 A319444

Keyword

nonn,base

Author

Seiichi Manyama, Sep 19 2018

Status

approved