A373679 Sums of maximal antiruns of non-prime-powers.

43, 53, 21, 163, 34, 35, 74, 39, 126, 45, 144, 51, 106, 55, 56, 57, 180, 128, 134, 69, 216, 75, 76, 77, 324, 85, 86, 87, 178, 91, 92, 93, 94, 95, 194, 99, 306, 105, 324, 111, 226, 115, 116, 117, 118, 119, 242, 123, 379, 262, 133, 134, 135, 414, 141, 142, 143

Offset: 1

Author

Gus Wiseman, Jun 17 2024

Keywords

• nonn

Comments

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

Examples

			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
  51
  52  54
  55
  56
  57
  58  60  62
  63  65
		

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, min A120430, max A006549, length A373671.

Non-prime-power antiruns: A373679 (this sequence), 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, A054265, A067774, A071148, A251092, A371201, A373401, A373669.

Programs

Mathematica

Total/@Split[Select[Range[100],!PrimePowerQ[#]&],#1+1!=#2&]//Most