A251416 a(n) = smallest number not in {A098550(1), A098550(2), ..., A098550(n)}.

2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 10, 11, 11, 11, 11, 11, 11, 13, 17, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31

Offset: 1

Author

N. J. A. Sloane, Dec 03 2014

Keywords

• nonn

Comments

a(n) = smallest missing number in A098550 once we have found A098550(n).

Bradley Klee conjectures that after a(30)=18, all further terms are primes, that every prime appears, and the primes appear in increasing order.

References

• Bradley Klee, Posting to Sequence Fans Mailing List, Dec 03 2014

Links

• N. J. A. Sloane and Reinhard Zumkeller, Table of n, a(n) for n = 1..100000 (first 1000 terms from N. J. A. Sloane)

Crossrefs

Cf. A098550, A251415. See A251417 for lengths of runs.

Cf. A251595 (distinct terms).

Cf. A251546, A251549.

Programs

Haskell

import Data.List (delete)
a251416 n = a251416_list !! (n-1)
a251416_list = 2 : 3 : f 2 3 [4..] where
   f u v ws = h ws where
     h (x:xs) = if gcd x u > 1 && gcd x v == 1
                   then (head ws) : f v x (delete x ws) else h xs
-- Reinhard Zumkeller, Dec 05 2014

Maple

# This produces the first 100 terms. Uses b1 = list of terms in A098550, from b-file
b2:={$3..5000}:
b3:=[2]:
for i from 2 to 100 do
b2:=remove('x->x=b1[i]',b2):
b3:=[op(b3),b2[1]];
od:
b3;

Mathematica

terms = 100;
f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, terms-3];
a[1] = 2;
a[n_] := a[n] = For[k = a[n - 1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]];
Array[a, terms] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *)

Formula

a(n) = Min{A251546(n), A251549(n)}. - Reinhard Zumkeller, Dec 19 2014