A373670 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A373670

Numbers k such that the k-th run-length A110969(k) of the sequence of non-prime-powers (A024619) is different from all prior run-lengths.

12

1, 5, 7, 12, 18, 28, 40, 53, 71, 109, 170, 190, 198, 207, 236, 303, 394, 457, 606, 774, 1069, 1100, 1225, 1881, 1930, 1952, 2247, 2281, 3140, 3368, 3451, 3493, 3713, 3862, 4595, 4685, 6625, 8063, 8121, 8783, 12359, 12650, 14471, 14979, 15901, 17129, 19155

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

OFFSET

1,2

COMMENTS

The unsorted version is A373669.

LINKS

Table of n, a(n) for n=1..47.

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

So the a(n)-th runs begin:

1

14 15

20 21 22

33 34 35 36

54 55 56 57 58

MATHEMATICA

t=Length/@Split[Select[Range[10000], !PrimePowerQ[#]&], #1+1==#2&];

Select[Range[Length[t]], FreeQ[Take[t, #-1], t[[#]]]&]

CROSSREFS

For nonsquarefree runs we have A373199 (if increasing), firsts of A053797.

For squarefree antiruns see A373200, unsorted A373128, firsts of A373127.

For composite runs we have A373400, unsorted A073051, firsts of A176246.

For prime antiruns we have A373402.

For runs of non-prime-powers:

- length A110969, firsts A373669, sorted A373670 (this sequence):

For runs of prime-powers:

- length A174965

A000961 lists the powers of primes (including 1).

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

A361102 lists the non-prime-powers, without 1 A024619.

Cf. A005381, A008864, A014963, A027833, A038664, A356068, A373401, A373574.

Sequence in context: A314311 A031144 A314312 * A160243 A373669 A247027

Adjacent sequences: A373667 A373668 A373669 * A373671 A373672 A373673

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 15 2024

STATUS

approved