A110969 Length of the runs of ones in A014963.

1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 4, 3, 1, 3, 1, 3, 5, 1, 2, 2, 3, 1, 5, 1, 1, 5, 7, 3, 1, 3, 1, 3, 7, 3, 1, 2, 5, 1, 9, 1, 5, 5, 3, 1, 3, 5, 1, 9, 1, 3, 1, 11, 11, 3, 1, 3, 5, 1, 1, 7, 4, 5, 5, 1, 5, 3, 1, 5, 3, 13, 3, 1, 3, 13, 5, 5, 3, 1, 3, 5, 1, 5, 5, 5, 3, 5, 7, 3, 7

Offset: 1

Author

Franz Vrabec, Sep 27 2005

Keywords

• nonn

Comments

Unbounded sequence.

From A373669 we see that 10 first appears at a(28195574) = 10.

Also run-lengths of non-prime-powers (assuming 1 is not a prime-power), where a run of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by one. Also nonzero differences of consecutive prime-powers minus one. - Gus Wiseman, Jun 18 2024

Examples

			a(5)=2 because the fifth run of ones in A014963 is of length 2.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014963.

Positions of first appearances are A373670, sorted A373669.

For runs of prime-powers:

- length A174965, antiruns A373671

- min A373673, antiruns A120430

- max A373674, antiruns A006549

- sum A373675, antiruns A373576

For runs of non-prime-powers:

- length A110969 (this sequence), antiruns A373672

- min A373676, antiruns A373575

- max A373677, antiruns A255346

- sum A373678, antiruns A373679

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

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).

Various run-lengths: A053797, A120992, A175632, A176246.

Various antirun-lengths: A027833, A373127, A373403, A373409.

Cf. A001359, A008864, A067774, A251092.

Programs

Mathematica

Length /@ SplitBy[Table[Exp[MangoldtLambda[n]], {n, 400}], # != 1 &][[ ;; -1 ;; 2]] (* Michael De Vlieger, Mar 21 2024 *)
DeleteCases[Differences[Select[Range[100],PrimePowerQ]]-1,0] (* Gus Wiseman, Jun 18 2024 *)

PARI

\\ b(n) returns boolean of A014963(n) == 1.
b(n)={my(t); !isprime(if(ispower(n, ,&t), t, n))}
seq(n)={my(k=1, i=0, L=List()); while(#Lk, listput(L, i-k)); k = i+1)); Vec(L)} \\ Andrew Howroyd, Jan 02 2020

Extensions

Terms a(41) and beyond from Andrew Howroyd, Jan 02 2020