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%I #13 Jun 17 2021 05:54:54
%S 5,19,43,31,67,541,193,157,1213,811,487,2371,2,1543,733,1319,1291,
%T 1753,1621,2713,13,1231,2833,2053,1801,3313,5011,821,2467,5101,3253,
%U 8573,3637,1553,15427,5521,3191,9173,7237,10531,11071,6271,9103,15727,7993
%N Least initial value for an Euclid/Mullin sequence whose 4th term is prime(n). prime(1)=2 is never a fourth term, so offset=2.
%F a(n) = Min_{k} A051614(k) = prime(n).
%e 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.
%e 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.
%e 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.
%t 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}]
%Y Cf. A000945, A051308-A051334, A094460, A094464.
%K nonn
%O 2,1
%A _Labos Elemer_, May 10 2004
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