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A085084 Smallest number not yet used which is not a prime but is relatively prime to the previous term. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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-Fran├žois Alcover, Jul 17 2012 *)

PROG

(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

CROSSREFS

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

Cf. A000027.

Sequence in context: A140808 A163642 A220533 * A248390 A075570 A236630

Adjacent sequences:  A085081 A085082 A085083 * A085085 A085086 A085087

KEYWORD

easy,nice,nonn

AUTHOR

Amarnath Murthy, Jul 02 2003

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

STATUS

approved

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Last modified October 24 00:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)