OFFSET
1,2
COMMENTS
No further terms found using primes up to 10^12. - Douglas McNeil, Jan 14 2011
According to Thomas R. Nicely (see Links) the next term, if it exists, must correspond to a gap occurring between primes greater than 4*10^18. - Giovanni Resta, Jan 06 2013
LINKS
Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Veikko Pohjola et al., Differences of consecutive primes, seqfan list, Jan 2011.
EXAMPLE
For k >= 2, consider A028334(k) = (1/2) * (prime(k+1) - prime(k)), half the k-th gap between primes. (We ignore g(1), which would equal 1/2.)
Then, using k=2,...,24 (and up to k=29), all the values 1,2,3 and 4 occur. Therefore, a(4)=4 is in the sequence.
However, for k=30 a new gap of 14 = 2*7 occurs, thus creating the "holes" (missing values) g=5 and g=6. The list of gaps has holes until one reaches k=46: At that moment all values g=1,...,7, and no other values occur. (This remains true up to k=98.) Therefore, a(5)=7 is in the list.
For more examples, see link to posts by Veikko Pohjola.
PROG
(PARI) my(p=2, L=1, l=1, g=1, o); while(p=nextprime(1+(o=p)), bittest(g, (p-o)\2) & next; my(a=(p-o)\2); g+=1<<a; a>L & L=a; l==a || next; while(bittest(g, l++), ); l>L & print1( L, ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 16 2011
STATUS
approved