A373674 - OEIS

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A373674

Last element of each maximal run of powers of primes (including 1).

22

5, 9, 11, 13, 17, 19, 23, 25, 27, 29, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239

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OFFSET

1,1

COMMENTS

A run of a sequence (in this case A000961) is an interval of positions at which consecutive terms differ by one.

The first element of the same run is A373673.

Consists of all powers of primes k such that k+1 is not a power of primes.

LINKS

Table of n, a(n) for n=1..58.

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

EXAMPLE

The maximal runs of powers of primes begin:

1 2 3 4 5

7 8 9

11

13

16 17

19

23

25

27

29

31 32

37

41

43

47

49

MATHEMATICA

pripow[n_]:=n==1||PrimePowerQ[n];

Max/@Split[Select[Range[nn], pripow], #1+1==#2&]//Most

CROSSREFS

For prime antiruns we have A001359, min A006512, length A027833.

For composite runs we have A006093, min A008864, length A176246.

For prime runs we have A067774, min A025584, length A251092 or A175632.

For squarefree runs we have A373415, min A072284, length A120992.

For nonsquarefree runs we have min A053806, length A053797.

For runs of prime-powers:

- length A174965

- max A373674 (this sequence)

For runs of non-prime-powers:

- length A110969 (firsts A373669, sorted A373670)

For antiruns of prime-powers:

- length A373671

For antiruns of non-prime-powers:

- length A373672

A000961 lists all powers of primes (A246655 if not including 1).

A025528 counts prime-powers up to n.

A057820 gives first differences of consecutive prime-powers, gaps A093555.

A361102 lists all non-prime-powers (A024619 if not including 1).

Cf. A000040, A005381, A007674, A014963, A068780, A068781, A073051, A373400.

Sequence in context: A335486 A347771 A294277 * A043721 A043727 A043731

Adjacent sequences: A373671 A373672 A373673 * A373675 A373676 A373677

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 16 2024

STATUS

approved