A175077 Final number reached by iterating r -> A049711(r) starting at r = n.

1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1

Offset: 1

Author

Jaroslav Krizek, Jan 23 2010

Keywords

• nonn

Comments

See A175071 for starting n that reach 1, and A175072 for starting n that reach 2.

Examples

			Iteration procedure for n = 6: 6 mod 5 = 1 = a(6).
Iteration procedure for n = 7: 7 mod 5 = 2 = a(7).
		

Crossrefs

Cf. A049711, A121559, A151799, A175071, A175072.

Programs

Maple

A151799 := proc(n) prevprime(n) ; end proc:
A049711 := proc(n) if n <=2 then n; else n-A151799(n) ; end if; end proc:
A175077 := proc(n) local r ; r := n ; while r > 2 do r := A049711(r) ; end do: r ; end proc:
seq(A175077(n),n=1..100) ; # R. J. Mathar, Feb 19 2010

Mathematica

f[n_] := Switch[n, 1, 1, 2, 2, _, n - NextPrime[n, -1]];
a[n_] := FixedPoint[f, n];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 13 2023 *)

Formula

a(A175071(k)) = 1; a(A175072(k)) = 2, any k. - R. J. Mathar, Feb 19 2010

a(n) = A121559(n-1) + 1 for n >= 2. - Pontus von Brömssen, Jul 31 2022

Extensions

More terms from R. J. Mathar, Feb 19 2010