[seqfan] Differences of consecutive primes

[Veikko Pohjola]

Maybe I was not clear enough in presenting what I am searching for.

I give two more examples

738<=K<=1182 -> {1,2,3,...,15,16,17} -> a(6)=17
1183<=K<=1830 -> {1,2,3,...,16,17,18} -> a(7)=18



The Mathematica program of Harvey is ok but gives actually the results 
above. Thus, for instance, Range[n], {n, 31, 34} gives {1,2,3,4,7} and 
Range[n], {n, 35, 46} gives {1,2,3,4,5,7}, which means that there is a gap 
in the K-values from 30 to 45 which does not produce perfect sequences of 
small integers, which are what I am looking for. Also the existence of the 
gaps from 99 to 737 and from 1831 to somewhere are supported by the program.

I am still wondering would there be a continuation for the sequence 1, 2, 3, 
4, 7, 17, 18,.
Veikko