A373673 - OEIS

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A373673

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

23

1, 7, 11, 13, 16, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 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

1,2

COMMENTS

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

The last element of the same run is A373674.

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];

Min/@Split[Select[Range[100], pripow], #1+1==#2&]//Most

CROSSREFS

For composite antiruns we have A005381, max A068780, length A373403.

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

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

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

For runs of prime-powers:

- length A174965

- min A373673 (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, A007674, A014963, A053806, A054265, A068781, A072284, A073051, A120992, A373400.

Sequence in context: A374082 A172120 A112090 * A103487 A175811 A373140

Adjacent sequences: A373670 A373671 A373672 * A373674 A373675 A373676

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 15 2024

STATUS

approved