This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A179985 #52 Dec 23 2024 14:53:42
%S A179985 1,2,3,4,7,17,18,77
%N A179985 Numbers N such that {A028334(2), ..., A028334(K)} = {1,...,N} for some K >= 2, where A028334(k) = (prime(k+1) - prime(k))/2.
%C A179985 No further terms found using primes up to 10^12. - Douglas McNeil, Jan 14 2011
%C A179985 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
%H A179985 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]
%H A179985 Veikko Pohjola et al., <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2011-January/006850.html">Differences of consecutive primes</a>, seqfan list, Jan 2011.
%e A179985 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.)
%e A179985 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.
%e A179985 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.
%e A179985 For more examples, see link to posts by Veikko Pohjola.
%o A179985 (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, ", "))
%Y A179985 Cf. A000230, A187779.
%K A179985 nonn
%O A179985 1,2
%A A179985 _M. F. Hasler_, Jan 16 2011