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.

A060087 Numbers k such that k^2 is a palindromic square with an asymmetric root.

Original entry on oeis.org

1109111, 110091011, 111091111, 10109901101, 10110911101, 11000910011, 11010911011, 11100910111, 1010099010101, 1010109110101, 1011099011101, 1100009100011, 1101009101011, 1110009100111, 100109990011001
Offset: 1

Views

Author

Patrick De Geest, Feb 15 2001

Keywords

Comments

With 'asymmetric' is meant almost palindromic with a 'core' (pseudo-palindromic). The core '09' when transformed into '1n' (n=-1) makes the base number palindromic. E.g., 1109111 is in fact 11_09_111 -> 11_(10-1)_111 -> 11_1n_111 -> 111n111 and palindromic. Similarly core 099 becomes 10n, core 0999 becomes 100n, etc.

References

  • M. Keith, "Classification and Enumeration of Palindromic Squares," Journal of Recreational Mathematics, 22:2, pp. 124-132, 1990.

Links

Crossrefs

Cf. A060088, A007573, A059744, A059745.

A060088 Palindromic squares with an asymmetric square root.

Original entry on oeis.org

1230127210321, 12120030703002121, 12341234943214321, 102210100272001012201, 102230523292325032201, 121020021070120020121, 121240161292161042121, 123230205292502032321, 1020300010207020100030201
Offset: 1

Views

Author

Patrick De Geest, Feb 15 2001

Keywords

Comments

With 'asymmetric' is meant almost palindromic with a 'core' (pseudo-palindromic). The core '09' when transformed into '1n' (n=-1) makes the base number palindromic. E.g., 1109111 is in fact 11_09_111 -> 11_(10-1)_111 -> 11_1n_111 -> 111n111 and palindromic. Similarly core 099 becomes 10n, core 0999 becomes 100n, etc.

References

  • M. Keith, "Classification and Enumeration of Palindromic Squares," Journal of Recreational Mathematics, 22:2, pp. 124-132, 1990.

Links

Crossrefs

Cf. A060087, A007573, A059744, A059745.

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 1-4 of 4 results.

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

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