A179985 Numbers N such that {A028334(2), ..., A028334(K)} = {1,...,N} for some K >= 2, where A028334(k) = (prime(k+1) - prime(k))/2.

1, 2, 3, 4, 7, 17, 18, 77

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

Table of n, a(n) for n=1..8.

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) p=2; L=l=g=1; while(p=nextprime(1+o=p), bittest(g, (p-o)\2) & next; a=(p-o)\2; g+=1<<a; a>L & L=a; l==a | next; while(bittest(g, l++), ); l>L & print1( L ", "))

Crossrefs

Cf. A000230, A187779.

Sequence in context: A254432 A027362 A068194 * A338928 A110705 A139439

Adjacent sequences: A179982 A179983 A179984 * A179986 A179987 A179988

Keyword

nonn

Author

M. F. Hasler, Jan 16 2011

Status

approved