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 1-6 of 6 results.

A118651 Numbers k such that k^2 is a palindrome when written in base 17.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 12, 18, 28, 36, 84, 108, 290, 307, 324, 341, 580, 597, 614, 1080, 1614, 1740, 1842, 2616, 3378, 3480, 3720, 4344, 4824, 4914, 5220, 5526, 6408, 9828, 10134, 10440, 14472, 17944, 19336, 24360, 27624, 29484, 31320, 33144, 33960
Offset: 1

Views

Author

Neven Juric (neven.juric(AT)apis-it.hr), May 12 2006

Keywords

Examples

			E.g. 4^2 = 16_10 = G_16, 6^2 = 36_10 = 22_17, etc.

Links

Crossrefs

Cf. A029984 for base 3, A029986 for base 4, A029988 for base 5, A029990 for base 6, A029992 for base 7, A029805 for base 8, A029994 for base 9, A002778 for base 10, A029996 for base 11, A029733 for base 16
Cf. also A016106, A028818, A059744, A059745.

A059744 Numbers k such that k^2 is a palindromic square of sporadic type.

Original entry on oeis.org

26, 264, 307, 836, 2285, 2636, 22865, 24846, 30693, 798644, 1042151, 1270869, 2012748, 2294675, 3069307, 11129361, 12028229, 12866669, 30001253, 64030648, 306930693, 2062386218, 2481623254, 10106064399, 10207355549, 13579355059, 22865150135, 30101273647, 30693069307
Offset: 1

Views

Author

N. J. A. Sloane, Feb 21 2001

Keywords

References

  • C. Ashbacher, More on palindromic squares, J. Rec. Math. 22, no. 2 (1990), 133-135. [A scan of the first page of this article is included with the last page of the Keith (1990) scan]
  • J. K. R. Barnett, "Tables of Square Palindromes in Bases 2 and 10," Journal of Recreational Mathematics, 23:1, pp. 13-18, 1991.
  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 26, pp 10, Ellipses, Paris 2008.
  • M. Keith, "Classification and Enumeration of Palindromic Squares," Journal of Recreational Mathematics, 22:2, pp. 124-132, 1990.
  • R. Ondrejka, "A Palindrome (151) of Palindromic Squares," Journal of Recreational Mathematics, 20:1, pp. 68-71, 1988.

Links

Crossrefs

Cf. A059745, A016106, A028818, A060087.

Programs

  • Mathematica
    Select[Range[1042151], ! PalindromeQ[#] && PalindromeQ[#^2] &] (* Michael De Vlieger, Oct 03 2023, not suitable for terms > 1042151, needs amendment for larger terms *)

Extensions

More terms from WorldOfNumbers website, communicated by Hugo Pfoertner, Oct 03 2023

A028818 Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots.

Original entry on oeis.org

676, 69696, 94249, 5221225, 6948496, 522808225, 617323716, 942060249, 1086078706801, 1615108015161, 4051154511504, 5265533355625, 9420645460249, 123862676268321, 144678292876441, 165551171155561, 900075181570009, 94206450305460249
Offset: 1

Views

Author

Patrick De Geest

Keywords

Links

Crossrefs

Cf. A016106.

A059745 Palindromic squares of sporadic type.

Original entry on oeis.org

676, 69696, 94249, 698896, 5221225, 6948496, 522808225, 617323716, 942060249, 637832238736, 1086078706801, 1615108015161, 4051154511504, 5265533355625, 9420645460249, 123862676268321, 144678292876441, 165551171155561, 900075181570009, 4099923883299904, 94206450305460249
Offset: 1

Views

Author

N. J. A. Sloane, Feb 21 2001

Keywords

References

  • C. Ashbacher, More on palindromic squares, J. Rec. Math. 22, no. 2 (1990), 133-135. [A scan of the first page of this article is included with the last page of the Keith (1990) scan]
  • J. K. R. Barnett, "Tables of Square Palindromes in Bases 2 and 10," Journal of Recreational Mathematics, 23:1, pp. 13-18, 1991.
  • M. Keith, "Classification and Enumeration of Palindromic Squares," Journal of Recreational Mathematics, 22:2, pp. 124-132, 1990.
  • R. Ondrejka, "A Palindrome (151) of Palindromic Squares," Journal of Recreational Mathematics, 20:1, pp. 68-71, 1988.

Links

Crossrefs

Cf. A059744, A016106, A028818, A060088.

Formula

a(n) = A059744(n)^2. - Hugo Pfoertner, Oct 03 2023

Extensions

More terms from WorldOfNumbers website, communicated by Hugo Pfoertner, Oct 03 2023

A065378 Primes p such that p^2 is a palindromic square.

Original entry on oeis.org

2, 3, 11, 101, 307, 30001253, 100111001, 110111011, 111010111, 111091111, 1011099011101, 1100011100011, 1100101010011, 1101010101011, 100110101011001, 100110990111001, 101000010000101, 101011000110101, 101110000011101
Offset: 1

Views

Author

Patrick De Geest, Nov 03 2001

Keywords

Comments

Record prime base number of a sporadic palindromic square is 13661181333262459.

Examples

			E.g. a(6) = 900075181570009 = p^2 with p = 30001253 and prime.

Links

Crossrefs

Cf. A065379, A002778, A002779, A034822, A028816, A016106, A059744, A016113, A007573.

Programs

  • Mathematica
    t={}; Do[p=Prime[n]; If[FromDigits[Reverse[IntegerDigits[p^2]]]==p^2,AppendTo[t,p]],{n,10^7}]; t (* Jayanta Basu, May 11 2013 *)

Extensions

Corrected by Jayanta Basu, May 11 2013

A065379 Palindromic squares with a prime root.

Original entry on oeis.org

4, 9, 121, 10201, 94249, 900075181570009, 12124434743442121, 12323244744232321, 12341234943214321, 1022321210249420121232201, 1210024420147410244200121, 1210222232227222322220121
Offset: 1

Views

Author

Patrick De Geest, Nov 03 2001

Keywords

Comments

Record sporadic palindromic square with a prime root is 186627875420278656872024578726681.

Examples

			a(6) = 900075181570009 = p^2 with p = 30001253, a prime.

Links

Crossrefs

Cf. A065378, A002778, A002779, A034822, A028816, A016106, A059744, A016113, A007573.
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.