Building Brilliant Numbers

I shouldn't let the opportunity go by to make a note of today and tomorrow's numbers: 25094 and 25095. Both these numbers belong to the OEIS sequence A108770: numbers n such that \(n^2 + (n+1)^2 \) is a brilliant number. The sequence proceeds:

3, 10, 15, 20, 27, 37, 59, 92, 105, 120, 152, 155, 175, 190, 215, 219, 242, 245, 254, 255, 277, 300, 302, 307, 325, 337, 362, 365, 370, 402, 415, 614, 930, 944, 987, 1049, 1059, 1112, 1192, 1204, 1210, 1220, 1265, 1312, 1344, 1360, 1374, 1449, 1460, 1504, 1527, ...

As can be seen, such numbers are relatively common. 92 is given as an example \( 92^2 + 93^2 = 17113 = 109*157 \) as both of its factors have three digits. 25094 is also in this sequence because \( 25094^2+25095^2 = 1259467861 = 23873×52757 \) but so also is 25095 because \( 25095^2+25096^2 = 1259568241 = 29401×42841 \). These consecutive pairs are relatively rare and those listed are (254,255), (4099,4100), (11159,11160), (25094, 25095), (31754,31755) and (40189,40190) with the conjecture that there are infinitely many of such pairs.

It's a bit of a wait until the next pair (31754 and 31755) but hopefully I'll be around to greet them.