OFFSET
1,2
COMMENTS
EXAMPLE
The odd primes begin:
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
with antiruns (differing by > 2):
(3), (5), (7,11), (13,17), (19,23,29), (31,37,41), (43,47,53,59), ...
with lengths:
1, 1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, 4, 3, 5, 3, 4, 5, 12, ...
which have runs:
(1,1), (2,2), (3,3), (4), (3), (6), (2), (5), (2), (6), (2,2), (4), ...
with lengths:
2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
with sorted positions of first appearances a(n).
MATHEMATICA
t=Length/@Split[Length /@ Split[Select[Range[3, 10000], PrimeQ], #1+2!=#2&]];
Select[Range[Length[t]], FreeQ[Take[t, #-1], t[[#]]]&]
CROSSREFS
The unsorted version is A373827.
A000040 lists the primes.
A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
A046933 counts composite numbers between primes.
A065855 counts composite numbers up to n.
A071148 gives partial sums of odd primes.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 22 2024
STATUS
approved