A175851 a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n.

1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4

Offset

1,4

Comments

Sequence is cardinal and not fractal. Cardinal sequence is sequence with infinitely many times occurring all natural numbers. Fractal sequence is sequence such that when the first instance of each number in the sequence is erased, the original sequence remains.

Ordinal transform of the nextprime function, A151800(1..) = 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, ..., also ordinal transform of A304106. - Antti Karttunen, Jun 09 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(1) = 1, a(n) = n - A007917(n) + 1 for n >= 2. a(1) = 1, a(2) = 1, a(n) = n - A151799(n+1) + 1 for n >= 3.

a(n) = Sum_{i=1..n} floor(pi(i)/pi(n)), for n>1 with pi(n) = A000720(n). - Ridouane Oudra, Jun 24 2024

a(n) = A049711(n+1), for n>1. - Ridouane Oudra, Jul 16 2024

Mathematica

a[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
Array[a, 100] (* Jean-François Alcover, Dec 19 2021 *)

Prog

(PARI) A175851(n) = if(1==n, n, 1 + n - precprime(n)); \\ Antti Karttunen, Mar 04 2018

Crossrefs

Cf. A000720, A007917, A008578, A151799, A151800, A305300.

Cf. A065358 for another way of visualizing prime gaps.

Cf. A304106 (ordinal transform of this sequence).

Cf. A049711.

Sequence in context: A160975 A305300 A330241 * A049711 A137293 A378636

Adjacent sequences: A175848 A175849 A175850 * A175852 A175853 A175854

Keyword

nonn,look

Author

Jaroslav Krizek, Sep 29 2010

Status

approved