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

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

Offset: 1

Author

Patrick De Geest, Feb 15 2001

Keywords

• nonn
• base

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

• Hugo Pfoertner, Table of n, a(n) for n = 1..10032
• Patrick De Geest, Subsets of Palindromic Squares
• IBM Research Ponder This, Non-palindromic numbers with palindromic squares, October 2023 - Challenge.

Crossrefs

Cf. A060088, A007573, A059744, A059745.