A175856 a(n) = a(n-1) - 1 if n is composite, a(n) = n otherwise.

1, 2, 3, 2, 5, 4, 7, 6, 5, 4, 11, 10, 13, 12, 11, 10, 17, 16, 19, 18, 17, 16, 23, 22, 21, 20, 19, 18, 29, 28, 31, 30, 29, 28, 27, 26, 37, 36, 35, 34, 41, 40, 43, 42, 41, 40, 47, 46, 45, 44, 43, 42, 53, 52, 51, 50, 49, 48, 59, 58, 61, 60, 59, 58, 57, 56, 67, 66

Offset: 1

Author

Jaroslav Krizek, Sep 29 2010

Keywords

• nonn
• easy

Comments

a(n) = n for noncomposite n, a(n) = 2 * (previous prime (n)) - n for composite n.

See A175859 - absent positive integers (pairs of consecutive numbers) in sequence: 8, 9, 14, 15, 24, 25, 32, 33, ...

a(n) = A075365(n) except at n = 1 and n = 10. - Alexandre Herrera, Nov 11 2023

Examples

			a(7) = 7 (7 is a noncomposite number), a(8) = 2*7 - 8 = 6 (8 is composite).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A008578, A175857, A175858, A175859, A175860, A175861, A175862, A075365.

Programs

Maple

a:= proc(n) option remember;
      `if`(n=1 or isprime(n), n, a(n-1)-1)
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Jun 22 2021

Mathematica

a[1] := 1; a[n_] := a[n] = If[PrimeQ[n], n, a[n - 1] - 1] (* Ben Branman, Jan 02 2011 *)
nxt[{n_,a_}]:={n+1,If[CompositeQ[n+1],a-1,n+1]}; NestList[nxt,{1,1},70][[All,2]] (* Harvey P. Dale, Jan 01 2023 *)

PARI

a(n)=if(n==1, 1, 2*precprime(n)-n) \\ Charles R Greathouse IV, Apr 22 2022~

Extensions

Corrected by Jaroslav Krizek, Oct 01 2010