A373675 Sums of maximal runs of powers of primes A000961.

15, 24, 11, 13, 33, 19, 23, 25, 27, 29, 63, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 255, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239

Offset

1,1

Comments

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

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];
Total/@Split[Select[Range[nn], pripow], #1+1==#2&]//Most

Crossrefs

A000040 lists the primes, differences A001223.

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).

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

Prime-power runs: A373675, min A373673, max A373674, length A174965.

Non-prime-power runs: A373678, min A373676, max A373677, length A110969.

Prime-power antiruns: A373576, min A120430, max A006549, length A373671.

Non-prime-power antiruns: A373679, min A373575, max A255346, length A373672.

Cf. A005117, A014963, A029707, A038664, A046933, A054265, A065855, A071148, A293697, A371201.

Sequence in context: A111151 A361340 A166657 * A059144 A274339 A343053

Adjacent sequences: A373672 A373673 A373674 * A373676 A373677 A373678

Keyword

nonn

Author

Gus Wiseman, Jun 16 2024

Status

approved