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

1,1

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)

Formula

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

Prog

(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

Crossrefs

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

Cf. A251595 (distinct terms).

Cf. A251546, A251549.

Sequence in context: A087846 A067854 A194214 * A372079 A087829 A078474

Adjacent sequences: A251413 A251414 A251415 * A251417 A251418 A251419

Keyword

nonn

Author

N. J. A. Sloane, Dec 03 2014

Status

approved