MathDB

interesting sequence

Source: bmo 1988

April 23, 2007

number theoryprime numbersnumber theory proposed

Problem Statement

Let

(a_{n})_{n\geq 1}

be a sequence defined by

a_{n}=2^{n}+49

. Find all values of

n

such that

a_{n}=pg, a_{n+1}=rs

, where

p,q,r,s

are prime numbers with

p<q, r<s

and

q-p=s-r

.

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