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

1,1

Comments

Problem proposed on French site Diophante (see link).

Links

Table of n, a(n) for n=1..17.

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

Example

(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.

Crossrefs

Equals A238237 \ A350870.

A059988 \ {0, 81} is a subsequence.

Sequence in context: A222814 A156735 A227489 * A113937 A036353 A174769

Adjacent sequences: A350915 A350916 A350917 * A350919 A350920 A350921

Keyword

nonn,base

Author

Bernard Schott, Jan 22 2022

Status

approved