OFFSET
2,1
FORMULA
a(n) = Min_{k} A051614(k) = prime(n).
EXAMPLE
n=14: prime(14) = 43 and an Euclid-Mullin sequence started with a(14) = 2 = prime(1) is {2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...} is A000945, the prototype EM-sequence.
n=7: a(7) = prime(100) = 541, with EM sequence as follows: {541, 2, 3, 17, 139, 7, 1871, 100457892907, 19, 11047, ...}, where the 4th term equals prime(n) = prime(7) = 17.
It is characteristic but not so simple congruence relations holds of term(1) mod term(4) form for various first or 4th primes, not necessarily smallest ones. See comment at A094464.
MATHEMATICA
a[x_]:=First[Flatten[FactorInteger[Apply[Times, Table[a[j], {j, 1, x-1}]]+1]]]; ta=Table[0, {20000}]; a[1]=1; Do[{a[1]=Prime[j], el=4}; ta[[j]]=a[el], {j, 1, 20000}] Table[Prime[Min[Flatten[Position[ta, Prime[w]]]]], {w, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 10 2004
STATUS
approved