A373575 - OEIS

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A373575

Numbers k such that k and k-1 both have at least two distinct prime factors. First element of the n-th maximal antirun of non-prime-powers.

22

1, 15, 21, 22, 34, 35, 36, 39, 40, 45, 46, 51, 52, 55, 56, 57, 58, 63, 66, 69, 70, 75, 76, 77, 78, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 105, 106, 111, 112, 115, 116, 117, 118, 119, 120, 123, 124, 130, 133, 134, 135, 136, 141, 142, 143, 144, 145

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

OFFSET

1,2

COMMENTS

The last element of the same antirun is given by A255346.

An antirun of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by more than one.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

The maximal antiruns 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

MATHEMATICA

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

CROSSREFS

Runs of prime-powers:

- length A174965

Runs of non-prime-powers:

- length A110969

Antiruns of prime-powers:

- length A373671

Antiruns of non-prime-powers:

- length A373672

- min A373575 (this sequence)

A000961 lists all powers of primes. A246655 lists just prime-powers.

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

A356068 counts non-prime-powers up to n.

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

Various run-lengths: A053797, A120992, A175632, A176246.

Various antirun-lengths: A027833, A373127, A373403, A373409.

Cf. A001359, A008864, A014963, A067774, A251092, A373669, A373670.

Sequence in context: A033708 A343821 A294171 * A306102 A177024 A325037

Adjacent sequences: A373572 A373573 A373574 * A373576 A373577 A373578

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 18 2024

STATUS

approved