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A093778 Primes p used as initial values for Euclid-Mullin sequences (variant A000945) instead of 2, such that all provide {p,2,3,5,7,11,13,q,...} initial segments in which the first six primes occur from 2nd to 7th terms.

%I A093778 #5 Oct 15 2013 22:32:23
%S A093778 99109,159169,189199,399409,459469,609619,669679,699709,819829,
%T A093778 1030039,1090099,1150159,1270279,1300309,1390399,1420429,1810819,
%U A093778 1870879,1930939,1960969,2021029,2051059,2141149,2201209,2261269,2321329
%N A093778 Primes p used as initial values for Euclid-Mullin sequences (variant A000945) instead of 2, such that all provide {p,2,3,5,7,11,13,q,...} initial segments in which the first six primes occur from 2nd to 7th terms.
%e A093778 Initial segments of Euclid-Mullin sequences provided by
%e A093778 a[33]=3132139, a[34] and a[35] initial values:
%e A093778 {3132139,2,3,5,7,11,13,94058134171}}
%e A093778 {3282289,2,3,5,7,11,13,59}},
%e A093778 {3372379,2,3,5,7,11,13,29}}
%t A093778 b[x_] :=First[Flatten[FactorInteger[Apply[Times, Table[b[j], {j, 1, x - 1}]] +1]]];b[1] = 1; Do[b[1] = Prime[j], el=8; If[Equal[Table[b[w], {w, 2, 7}], {2, 3, 5, 7, 11, 13}], Print[{j, Table[b[w], {w, 1, el}]}]], {j, 100000, 1000000}]
%Y A093778 Cf. A000945, A051308-A051334, A056756, A093777.
%K A093778 nonn
%O A093778 1,1
%A A093778 _Labos Elemer_, May 03 2004