A319389 -id:A319389 - cp's OEIS frontend

A319388 Non-palindromic squares.

16, 25, 36, 49, 64, 81, 100, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 529, 576, 625, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025

Offset: 1

Seiichi Manyama, Sep 18 2018

Intersection of A000290 and A029742. - Felix Fröhlich, Sep 18 2018

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A000290, A002113, A002779, A029742, A035090, A319389.

[n^2: n in [0..60] | not Intseq(n^2) eq Reverse(Intseq(n^2))]; // Vincenzo Librandi, Sep 19 2018

ispali:= proc(n) local L;
L:= convert(n,base,10);
L = ListTools:-Reverse(L)
end proc:
remove(ispali, [seq(i^2,i=1..100)]); # Robert Israel, Sep 18 2018

 pb10Q[n_]:=!Module[{idn10=IntegerDigits[n, 10]}, idn10==Reverse[idn10]]; Select[Range[0, 3100]^2, pb10Q] (* Vincenzo Librandi, Sep 19 2018 *)

terms(n) = my(i=0); for(k=0, oo, if(i==n, break); my(s=k^2, d=digits(s)); if(d!=Vecrev(d), print1(s, ", "); i++))
/* Print initial 50 terms as follows */
terms(50) \\ Felix Fröhlich, Sep 18 2018

A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

Original entry on oeis.org

1033364331, 1334633301, 1003303631331, 1331363033001, 1000330036301331, 1003033061330301, 1003333697667631, 1030331603303001, 1030637669664331, 1331036300330001, 1334669667360301, 1367667963333001, 1000033000363001331, 1000303030604030301, 1000333036964367631

Offset: 1

Patrick De Geest, Nov 15 1998

Cubes with trailing zeros are excluded.

			1011^3 = 1033364331 -> 1334633301 = 1101^3.
1003333697667631 is included because its cube root, 100111, when reversed (i.e., 111001) and cubed yields 1367667963333001.

P. De Geest, Palindromic Cubes
Eric Weisstein's World of Mathematics, Cubic Number
Index entry for sequences related to reversing digits of squares

Cf. A035090, A035125, A064021, A319389.

isok(n) = {if (ispower(n, 3, &k), dn = digits(n); if (Vecrev(dn) != dn, dk = Vecrev(digits(k)); rk = subst(Pol(dk, x), x, 10); digits(rk^3) == Vecrev(dn);););} \\ Michel Marcus, Oct 04 2015

More terms from Seiichi Manyama, Sep 18 2018

A319441 Cubes of non-palindromic numbers.

Original entry on oeis.org

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

Seiichi Manyama, Sep 19 2018

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

			2201^3 = 10662526601 is a term.

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.

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

[n^3: n in [0..65] | Intseq(n) ne Reverse(Intseq(n))]; // Vincenzo Librandi, Sep 19 2018

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 *)

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

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

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

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A319388 Non-palindromic squares.

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A035124 Nonpalindromic cubes remaining cubic which written backwards: take the cube root of n, reverse its digits, cube that and the result is n with its digits reversed.

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A319441 Cubes of non-palindromic numbers.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

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