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.

99109, 159169, 189199, 399409, 459469, 609619, 669679, 699709, 819829, 1030039, 1090099, 1150159, 1270279, 1300309, 1390399, 1420429, 1810819, 1870879, 1930939, 1960969, 2021029, 2051059, 2141149, 2201209, 2261269, 2321329

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Example

Initial segments of Euclid-Mullin sequences provided by
a[33]=3132139, a[34] and a[35] initial values:
{3132139,2,3,5,7,11,13,94058134171}}
{3282289,2,3,5,7,11,13,59}},
{3372379,2,3,5,7,11,13,29}}

Mathematica

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}]

Crossrefs

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

Sequence in context: A106776 A238296 A359345 * A234494 A255760 A255753

Adjacent sequences: A093775 A093776 A093777 * A093779 A093780 A093781

Keyword

nonn

Author

Labos Elemer, May 03 2004

Status

approved