login
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.
6

%I #5 Oct 15 2013 22:32:23

%S 99109,159169,189199,399409,459469,609619,669679,699709,819829,

%T 1030039,1090099,1150159,1270279,1300309,1390399,1420429,1810819,

%U 1870879,1930939,1960969,2021029,2051059,2141149,2201209,2261269,2321329

%N 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 Initial segments of Euclid-Mullin sequences provided by

%e a[33]=3132139, a[34] and a[35] initial values:

%e {3132139,2,3,5,7,11,13,94058134171}}

%e {3282289,2,3,5,7,11,13,59}},

%e {3372379,2,3,5,7,11,13,29}}

%t 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 Cf. A000945, A051308-A051334, A056756, A093777.

%K nonn

%O 1,1

%A _Labos Elemer_, May 03 2004