A350918 Numbers k = x.y which when split into two parts x and y of equal length, added and squared result in the same number k, '.' means concatenation, and the second part y starts with 0.

9801, 998001, 99980001, 9048004641, 9999800001, 923594037444, 989444005264, 999998000001, 7901234409876544, 8434234407495744, 8934133805179209, 9999999800000001, 999999998000000001, 79012345680987654321, 82644628100826446281, 83407877440792003584, 87138706300620940900

Offset: 1

Author

Bernard Schott, Jan 22 2022

Keywords

• nonn
• base

Comments

Problem proposed on French site Diophante (see link).

Examples

			(998+001)^2 = 999^2 = 998001, as x = 998 and y = 001 starts with 0, 998001 is a term.
(30+25)^2 = 55^2 = 3025, here x = 30 but y = 25 does not start with 0, hence 3025 is not a term.
		

Links

• Diophante, A1945 - Concaténations en tous genres (in French).

Crossrefs

Equals A238237 \ A350870.

A059988 \ {0, 81} is a subsequence.