cp's OEIS Frontend

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

%I A175851 #33 Aug 03 2024 19:20:46
%S A175851 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,
%T A175851 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,
%U A175851 3,4,1,2,1,2,3,4,5,6,1,2,3,4
%N A175851 a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n.
%C A175851 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.
%C A175851 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
%H A175851 Antti Karttunen, <a href="/A175851/b175851.txt">Table of n, a(n) for n = 1..65537</a>
%F A175851 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.
%F A175851 a(n) = Sum_{i=1..n} floor(pi(i)/pi(n)), for n>1 with pi(n) = A000720(n). - _Ridouane Oudra_, Jun 24 2024
%F A175851 a(n) = A049711(n+1), for n>1. - _Ridouane Oudra_, Jul 16 2024
%t A175851 a[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
%t A175851 Array[a, 100] (* _Jean-François Alcover_, Dec 19 2021 *)
%o A175851 (PARI) A175851(n) = if(1==n,n,1 + n - precprime(n)); \\ _Antti Karttunen_, Mar 04 2018
%Y A175851 Cf. A000720, A007917, A008578, A151799, A151800, A305300.
%Y A175851 Cf. A065358 for another way of visualizing prime gaps.
%Y A175851 Cf. A304106 (ordinal transform of this sequence).
%Y A175851 Cf. A049711.
%K A175851 nonn,look
%O A175851 1,4
%A A175851 _Jaroslav Krizek_, Sep 29 2010