A373673 First element of each maximal run of powers of primes (including 1).

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

Offset: 1

Author

Gus Wiseman, Jun 15 2024

Keywords

• nonn

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.

Examples

			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
		

Links

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

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)

- max A373674

- sum A373675

For runs of non-prime-powers:

- length A110969 (firsts A373669, sorted A373670)

- min A373676

- max A373677

- sum A373678

For antiruns of prime-powers:

- length A373671

- min A120430

- max A006549

- sum A373576

For antiruns of non-prime-powers:

- length A373672

- min A373575

- max A255346

- sum A373679

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.

Programs

Mathematica

pripow[n_]:=n==1||PrimePowerQ[n];
Min/@Split[Select[Range[100],pripow],#1+1==#2&]//Most