A373576 - OEIS

A373576

Sums of maximal antiruns of prime-powers.

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

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OFFSET

1,1

COMMENTS

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

LINKS

EXAMPLE

The maximal antiruns of powers of primes begin:

5 7

9 11 13 16

17 19 23 25 27 29 31

MATHEMATICA

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

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).

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jun 17 2024

EXTENSIONS

a(14) from Giorgos Kalogeropoulos, Jun 18 2024

STATUS

approved