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prime sequence, p_k = 2p_{k-1} + 1 or p_k = 2p_{k-1} - 1

Source: Dutch IMO TST2 2011 p4

January 10, 2020
recurrence relationSequenceprime numbersnumber theory

Problem Statement

Prove that there exists no in nite sequence of prime numbers p0,p1,p2,...p_0, p_1, p_2,... such that for all positive integers kk: pk=2pk−1+1p_k = 2p_{k-1} + 1 or pk=2pk−1−1p_k = 2p_{k-1} - 1.
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