

A036012


a(n) = smallest number > 1 such that a(1)a(2)...a(n) + 1 is prime.


12



2, 2, 3, 3, 2, 6, 3, 2, 4, 7, 7, 3, 8, 6, 2, 3, 6, 9, 6, 14, 19, 11, 4, 4, 19, 4, 13, 3, 10, 13, 15, 4, 11, 9, 2, 5, 26, 19, 52, 21, 20, 63, 4, 19, 17, 6, 29, 19, 3, 5, 51, 11, 14, 15, 7, 12, 44, 34, 7, 21, 32, 3, 22, 10, 19, 19, 7, 20, 4, 22, 4, 17, 35, 47, 40, 14, 5, 14, 36, 39, 16
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OFFSET

1,1


COMMENTS

Except for the first term, same as A084401.  David Wasserman, Dec 22 2004


LINKS

T. D. Noe, Table of n, a(n) for n = 1..300


FORMULA

Conjecture: a(n) = O(n).  Thomas Ordowski, Aug 08 2017


MAPLE

n := 1: while true do j := 2: while not isprime(j*n+1) do j := j+1: od: print(j): n := n*j: od:


MATHEMATICA

a[1] = 2; a[n_] := a[n] = Catch[For[an = 2, True, an++, If[PrimeQ[Product[a[k], {k, 1, n  1}]*an + 1], Throw[an]]]]; Table[a[n], {n, 1, 81}] (* JeanFrançois Alcover, Nov 27 2012 *)
nxt[{t_, n_}]:=Module[{k=2}, While[!PrimeQ[t*k+1], k++]; {t*k, k}]; NestList[ nxt, {2, 2}, 80][[All, 2]] (* Harvey P. Dale, Oct 03 2020 *)


CROSSREFS

Equals A084716(n+1)/A084716(n).
Cf. A036013, A084716, A084717, A084718.
Sequence in context: A303363 A045796 A127684 * A084401 A236465 A131619
Adjacent sequences: A036009 A036010 A036011 * A036013 A036014 A036015


KEYWORD

nonn,nice,easy


AUTHOR

Russell Easterly


EXTENSIONS

More terms from Erich Friedman
More terms from Jud McCranie, Jan 26 2000
Description corrected by Len Smiley


STATUS

approved



