By Doron Zeilberger

From time to time I offer to donate various sums to the OEIS in honor of the first prover of challenges.

Recently I got a barrage of emails from incoming Purdue freshman, Jaideep Sai Padhi, who met quite a few of them, using CLAUDE (both Fable and Opus). I am very happy to pay my gambling debts. The purpose of this web-page is to list all of them and sum-up how much I owe. Also to provide links to Padhi's github papers (and arxiv paper) that met these challenges.

• In this paper, written in 2012, joint with Shalosh B. Ekhad I asked for a rigorous proof of a certain recurrence that was found empirically. While I offered one cent, it is really worth $100. Here is Padhi's paper (written with Claude's help, of course)

• In this paper, written in 2025, joint with Tewodros Amdeberhan and Manuel Kauers, I offered $200 for the determination of the 5D Geode number G(1000,1000,1000,1000,1000). This challenge was met here

• In this note, written in 2018, joint with Shalosh B. Ekhad, I offered $100 for finding a chocolate bar that has three winning moves. Padhi, assisted by Claude, found it: a 10x42 chocolate bar, the three winning moves are: (5, 36), (7, 30), and (8, 26). This challenge was met here

• In this paper, written in 2020, joint with Manuel Kauers, I offered $200 each for the proofs of Conjectures 2a and 2b. This challenge was met here.

• In this paper, writtem in 2023, joint with George Spahn, Challenge 3 asked to prove that the sequences a_r,s(n), b_r,s(n) defined there are always P-recursive. I offered $300. This challege was met here

Adding this up, I owe $100+$200+$100+$200+$300=$900. Adding a `tip' of $100, this adds up to $1000. The donation was made. See the OEIS Foundation page (and do ^F for Padhi).

Added Aug. 19, 2026: Read Jaideep Sai Padhi's fascinating paper

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