A373826 Sorted positions of first appearances in the run-lengths (differing by 0) of the antirun-lengths (differing by > 2) of the odd primes.

1, 4, 38, 6781, 23238, 26100

Offset

1,2

Comments

Sorted positions of first appearances in A373820 (run-lengths of A027833 with 1 prepended).

Links

Table of n, a(n) for n=1..6.

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.

Cf. A001359, A006512, A025584, A037201, A038664, A054265, A067774, A176246, A251092, A373404, A373405, A373406.

Sequence in context: A030259 A218710 A286877 * A018860 A016484 A278052

Adjacent sequences: A373823 A373824 A373825 * A373827 A373828 A373829

Keyword

nonn,more,new

Author

Gus Wiseman, Jun 22 2024

Status

approved