[math-fun] Last 4 digits of S sum up to a square

Hello Math-fun, S = 1, 2, 4, 9,... If we want S to be the lexicographically earliest seq of distinct positive terms, we cannot have another start (like 1, 2, 3, X). The seq is finite — but how many terms can we plug in? I think we could extend S with 12: S = 1, 2, 4, 9, 12,... (the last 4 digits have sum 16 again — a square). Instead of 12 we could have extended S with 21, 30 or 999. This idea opens the way to a few variants, of course (sum k digits instead of 4, get a prime instead of a square), etc. Best, É. Catapulté de mon aPhone