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%I #25 Dec 19 2021 04:28:40
%S 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 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 3,4,1,2,1,2,3,4,5,6,1,2,3,4
%N a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n.
%C 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 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 Antti Karttunen, <a href="/A175851/b175851.txt">Table of n, a(n) for n = 1..65537</a>
%F 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.
%t a[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
%t Array[a, 100] (* _Jean-François Alcover_, Dec 19 2021 *)
%o (PARI) A175851(n) = if(1==n,n,1 + n - precprime(n)); \\ _Antti Karttunen_, Mar 04 2018
%Y Cf. A000720, A007917, A008578, A151799, A151800, A305300.
%Y Cf. A065358 for another way of visualizing prime gaps.
%Y Cf. A304106 (ordinal transform of this sequence).
%Y Cf. A049711.
%K nonn,look
%O 1,4
%A _Jaroslav Krizek_, Sep 29 2010
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