[seqfan] Differenes of conscutive primes

Veikko Pohjola veikko at nordem.fi
Thu Jan 13 20:05:05 CET 2011


Consider the halved differences of consecutive primes (Prime[k+1]-Prime[k])/2, k=2,3,4,.,K. Remove the duplicates and sort to obtain an ordered set {1,2,3,.,a(i)}of all natural numbers from 1 to a(i). The allowed numbers a(i) make up the following sequence: a(i) = 1, 2, 3, 4, 7, 17, 18,. 

 

Examples:

2<=K<=3 -> {1} -> a(1)=1

4<=K<=8 -> {1,2} -> a(2)=2

9<=K<=23 -> {1,2,3} -> a(3)=3

24<=K<=29 -> {1,2,3,4} ->a(4)=4

46<=K<=98 -> {1,2,3,4,5,6,7} -> a(5)=7

 

Might there be a continuation for the sequence a(i)?

Veikko



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