A085084 Smallest number not yet used which is not a prime but is relatively prime to the previous term.

1, 4, 9, 8, 15, 14, 25, 6, 35, 12, 49, 10, 21, 16, 27, 20, 33, 26, 45, 22, 39, 28, 51, 32, 55, 18, 65, 24, 77, 30, 91, 34, 57, 40, 63, 38, 69, 44, 75, 46, 81, 50, 87, 52, 85, 36, 95, 42, 115, 48, 119, 54, 121, 56, 93, 58, 99, 62, 105, 64, 111, 68, 117, 70, 123, 74, 125, 66

Offset: 1

Author

Amarnath Murthy, Jul 02 2003

Keywords

• easy
• nice
• nonn

Comments

Every composite number appears in this sequence. Eventually, every p^2 (p prime) will appear; if the smallest unused composite does not follow, it will appear no later than following the next p^2.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Sequences with related definitions: A051884, A064413, A075570, A163642, A240024.

Cf. A000027.

Programs

Haskell

import Data.List (find, delete)
import Data.Maybe (fromJust)
a085084 n = a085084_list !! (n-1)
a085084_list = 1 : f 1 a002808_list where
   f x cs = y : f y (delete y cs) where
            y = fromJust $ find ((== 1) . (gcd x)) cs
-- Reinhard Zumkeller, Dec 01 2012

Maple

# Corrected Maple program from Chen Zekai, Mar 23 2015, added by N. J. A. Sloane, Mar 23 2015
A085084 := proc (q) local a, b, i, n;if q = 1 then print(1); return;elif q = 2 then print(1); print(4); return;fi;a := {1, 4}; b := 4; i := 2; print(1); print(4);while i < q do for n from 6 to q^2 doif not isprime(n) and gcd(b, n) = 1 and {} = a intersect {n} thenb := n; a := a union {n}; i := i+1; print(n);break;fi; od; od; end:A085084(10000):

Mathematica

A085084 = {a[1]=1, a[2]=4}; a[n_] := a[n] = Catch[For[k = 6, True, k++, If[!PrimeQ[k] && !MemberQ[A085084, k] && CoprimeQ[a[n-1], k], AppendTo[A085084, k]; Throw[k]]]]; Table[ a[n], {n, 1, 68}] (* Jean-François Alcover, Jul 17 2012 *)

Extensions

Corrected and extended by Vladeta Jovovic, Jul 05 2003

Additional comments from Franklin T. Adams-Watters, Sep 19 2006

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar