A373819 - OEIS

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A373819

Run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 2, 4, 3, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 10, 2, 4, 1, 7, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 18, 3, 2, 1, 2, 1, 17, 2, 1, 2, 2, 1, 6, 1, 9, 1, 3, 1, 1, 1, 1, 1, 1, 1, 8, 1, 3, 1, 2, 2, 15, 1, 1, 1, 4, 1, 1, 1, 1, 1, 7, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Run-lengths of A251092.

LINKS

Table of n, a(n) for n=1..86.

Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers.

EXAMPLE

The odd primes begin:

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...

with runs:

3 5 7

11 13

17 19

29 31

41 43

59 61

71 73

with lengths:

3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, ...

which have runs beginning:

2 2

1 1

1 1 1 1

2 2

1 1 1

with lengths a(n).

MATHEMATICA

Length/@Split[Length/@Split[Select[Range[3, 1000], PrimeQ], #1+2==#2&]//Most]//Most

CROSSREFS

Run-lengths of A251092.

For antiruns we have A373820, run-lengths of A027833 (if we prepend 1).

Positions of first appearances are A373825, sorted A373824.

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.

For prime runs: A001359, A006512, A025584, A067774, A373405, A373406.

For composite runs: A005381, A054265, A068780, A373403, A373404.

Cf. A005117, A006560, A006562, A029707, A037201, A038664, A076259, A176246.

Sequence in context: A277231 A122934 A072170 * A368885 A294932 A327804

Adjacent sequences: A373816 A373817 A373818 * A373820 A373821 A373822

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 20 2024

STATUS

approved