login
A373826
Sorted positions of first appearances in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.
4
1, 4, 38, 6781, 23238, 26100
OFFSET
1,2
COMMENTS
Sorted positions of first appearances in A373820 (run-lengths of A027833 with 1 prepended).
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
Sorted positions of first appearances in A373820, cf. A027833.
For runs we have A373824 (unsorted A373825), sorted firsts of A373819.
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.
Sequence in context: A030259 A218710 A286877 * A018860 A016484 A278052
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 22 2024
STATUS
approved