A373677 - OEIS

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A373677

Last element of each maximal run of non-prime-powers.

22

1, 6, 10, 12, 15, 18, 22, 24, 26, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63, 66, 70, 72, 78, 80, 82, 88, 96, 100, 102, 106, 108, 112, 120, 124, 126, 130, 136, 138, 148, 150, 156, 162, 166, 168, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238

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

OFFSET

1,2

COMMENTS

We consider 1 to be a power of a prime and a non-prime-power, but not a prime-power.

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 A373676.

Consists of all non-prime-powers k such that k+1 is a prime-power.

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 non-prime-powers begin:

1

6

10

12

14 15

18

20 21 22

24

26

28

30

33 34 35 36

38 39 40

42

44 45 46

48

50 51 52

54 55 56 57 58

60

MATHEMATICA

Select[Range[100], !PrimePowerQ[#]&&PrimePowerQ[#+1]&]

CROSSREFS

See link for prime, composite, squarefree, and nonsquarefree runs/antiruns.

For runs of powers of primes:

- length A174965

For runs of non-prime-powers:

- length A110969 (firsts A373669, sorted A373670)

- max A373677 (this sequence)

For antiruns of prime-powers:

- length A373671

For antiruns of non-prime-powers:

- length A373672

A000961 lists all powers of primes. A246655 is just prime-powers so lacks 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, A038664, A068780, A068781, A073051, A373400, A373401.

Sequence in context: A362754 A143958 A294278 * A297366 A325472 A305188

Adjacent sequences: A373674 A373675 A373676 * A373678 A373679 A373680

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 16 2024

STATUS

approved