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Two Enigmatic Mathematica Programs

2025-06-29

This code showcases two Mathematica programs that generate numerical sequences. The first employs `Do` and `While` loops to iteratively build a sequence whose growth pattern depends on the position of preceding elements. The second program extends the sequence by cumulatively adding prior differences, continuing until the length surpasses 50. Both programs highlight Mathematica's capability in generating intricate sequences, with algorithms warranting further investigation.

Unresolved Mystery in the Sequence of Last Two Digits of 2^n

2025-03-20

Mathematicians have investigated the sequence of the last two digits of 2^n, finding that 2^n only conforms to this sequence when n takes specific values (congruent to 3, 6, 10, 11, or 19 mod 20). No additional conforming numbers have been found for n up to 50000. Further research reveals that checking digits from right to left until an odd digit is found requires checking at most the 18th digit. This discovery sparks further thought about the underlying pattern of this sequence and offers new avenues for mathematical exploration.