cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A115690 Squares whose digit reversal is a powerful(1) number (A001694).

Original entry on oeis.org

1, 4, 9, 100, 121, 144, 169, 400, 441, 484, 576, 676, 900, 961, 1089, 9801, 10000, 10201, 10404, 10609, 12100, 12321, 12544, 12769, 14400, 14641, 14884, 16900, 25281, 27225, 40000, 40401, 40804, 44100, 44521, 44944, 48400, 48841, 57600
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Comments

If x is a member, then so is 100*x. - Robert Israel, Mar 16 2020

Examples

			25281=159^2 and 18252=2^2*3^3*13^2 is powerful.

Links

Crossrefs

Subsequence of A115656.
A033294 is a subsequence, and the main entry for this sequence.
Cf. A001694, A115689.

Programs

  • Maple
    filter:= proc(n) local L,i,x;
  L:= convert(n,base,10);
  x:=add(L[-i]*10^(i-1),i=1..nops(L));
  andmap(t -> t[2]>=2, ifactors(x)[2]):
end proc:select(filter, [seq(i^2,i=1..10^4)]); # Robert Israel, Mar 16 2020
  • PARI
    is(k) = ispowerful(fromdigits(Vecrev(digits(k))));
select(is, vector(300, n, n^2)) \\ Michel Marcus, Nov 01 2022

Formula

Trivially, n^2 <= a(n) <= 100^(n-1). - Charles R Greathouse IV, Nov 01 2022

A110811 Perfect powers not a multiple of 10 whose digit reversal is also a perfect power (not necessarily with the same exponent, but with exponent > 1).

Original entry on oeis.org

1, 4, 8, 9, 121, 144, 169, 343, 441, 484, 676, 961, 1089, 1331, 9801, 10201, 10404, 10609, 12321, 12544, 12769, 14641, 14884, 40401, 40804, 44521, 44944, 48841, 69696, 90601, 94249, 96721, 698896, 1002001, 1004004, 1006009, 1022121, 1024144
Offset: 1

Views

Author

Amarnath Murthy, Aug 15 2005

Keywords

Comments

All palindromic perfect powers are trivial members, but there are infinitely many nontrivial members.

Examples

			12^2 =144, digit reversal of 144 is 441= 21^2. 12769=113^2, reversal(12769) = 96721 = 311^2.

Links

Crossrefs

This is a subset of A115656 and also a subset of A001597. See also A118895 to include terms with trailing zeros.

Programs

  • Mathematica
    Join[{1},Select[Range[11 10^5],Mod[#,10]!=0&&GCD@@FactorInteger[#][[All,2]]>1&&GCD@@FactorInteger[IntegerReverse[#]][[All,2]]>1&]] (* Harvey P. Dale, Jun 01 2018 *)

Extensions

Corrected and extended by Joshua Zucker, May 04 2006
Description and offset edited by Chai Wah Wu, Jun 06 2016

A118895 Numbers n with property that both n and its digit reversal are perfect powers (i.e., in A001597).

Original entry on oeis.org

1, 4, 8, 9, 100, 121, 144, 169, 343, 400, 441, 484, 676, 900, 961, 1000, 1089, 1331, 8000, 9801, 10000, 10201, 10404, 10609, 12100, 12321, 12544, 12769, 14400, 14641, 14884, 16900, 40000, 40401, 40804, 44100, 44521, 44944, 48400, 48841, 67600
Offset: 1

Views

Author

Joshua Zucker, May 04 2006

Keywords

Comments

An alternate version of A110811, which doesn't include the terms with trailing zeros.

Examples

			100 is in the sequence because 100 and 001 = 1 are both perfect powers;
44521 and 12544 are both in the sequence because both are perfect powers, 221^2 and 112^2.

Crossrefs

This sequence is a subset of both A115656 and A001597 and contains A110811.
Cf. A118715.

Extensions

Edited by N. J. A. Sloane, Oct 11 2008

A115655 Both n and the reverse of n are brilliant numbers (A078972).

Original entry on oeis.org

4, 6, 9, 121, 143, 169, 187, 319, 323, 341, 737, 767, 781, 913, 949, 961, 979, 989, 1273, 1343, 1691, 1843, 1961, 3431, 3481, 3721, 10201, 10807, 11413, 12769, 13231, 15049, 15151, 15251, 15347, 15707, 15857, 16171, 16837, 16867, 17161
Offset: 1

Views

Author

Giovanni Resta, Jan 28 2006

Keywords

Examples

			11413=101*113 and 31411=101*311.

Crossrefs

Cf. A078972, A115656, A085751.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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