A373576 Sums of maximal antiruns of prime-powers.

2, 3, 4, 12, 8, 49, 171, 2032, 5157, 3997521, 199713082, 561678378, 10122001905, 109934112352390774

Offset: 1

Author

Gus Wiseman, Jun 17 2024

Keywords

• nonn
• more

Comments

An antirun of a sequence (in this case A246655) is an interval of positions at which consecutive terms differ by more than one.

Examples

			The maximal antiruns of powers of primes begin:
   2
   3
   4
   5   7
   8
   9  11  13  16
  17  19  23  25  27  29  31
		

Links

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

Crossrefs

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

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 (this sequence), min A120430, max A006549, length A373671.

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

A000040 lists the primes, differences A001223.

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

A025528 counts prime-powers up to n.

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).

Cf. A001359, A014963, A027833, A029707, A038664, A067774, A251092, A293697, A371201, A373401, A373669.

Programs

Mathematica

Total/@Split[Select[Range[1000],PrimePowerQ],#1+1!=#2&]//Most

Extensions

a(14) from Giorgos Kalogeropoulos, Jun 18 2024