A193689 Even semiprime equivalent to the Euclid-Mullin sequence: a(1) = 4, a(n) = smallest semiprime divisor of product of previous terms plus 2.

4, 6, 26, 626, 34, 4762, 94, 10, 59450441556482, 37219202, 226, 14, 22, 359948158, 141142, 957030986, 82, 926, 46, 38, 86, 158, 262, 1126, 589928909976251551945088438, 4486, 2434, 62, 12398, 2367240322, 2942, 10430585378, 218, 394, 122, 74, 1042, 19862, 11197742711219732052345406

Offset

1,1

Comments

Except for 4, all terms are guaranteed to be squarefree.

Links

Table of n, a(n) for n=1..39.

Example

a(5) = 34 because the previous terms being 4, 6, 26 and 626, their product is 390624, and 390624 + 2 = 2 * 17 * 11489, the least semiprime divisor of which is 2 * 17 = 34.

Mathematica

smallestPrimeFactor[n_] := FactorInteger[n][[1, 1]]; semiprimePart[n_] := Module[{p = smallestPrimeFactor[n]}, p*smallestPrimeFactor[n/p]]; a = {4}; Do[AppendTo[a, semiprimePart[2 + Times @@ a]], {15}]; a (* T. D. Noe, Aug 02 2011 *)

Crossrefs

Cf. A000945, A000946, A100484.

Sequence in context: A176756 A054094 A123873 * A099941 A074120 A054265

Adjacent sequences: A193686 A193687 A193688 * A193690 A193691 A193692

Keyword

nonn

Author

Alonso del Arte and Jonathan Vos Post, Aug 02 2011

Extensions

More terms from Amiram Eldar, Feb 24 2021

Status

approved