A209321 Indices k for which A209312(k) = 2.

4, 5, 6, 7, 9, 11, 14, 19, 26, 38, 46, 62, 70, 74, 86, 94, 118, 134, 194, 206, 278, 286, 566, 598, 778, 842, 934, 1006, 1082, 1214, 1238, 1546, 1574, 1726, 1858, 2018, 2278, 2474, 2774, 3142, 3686

Offset: 1

Author

M. F. Hasler, Jan 19 2013

Keywords

• nonn
• more

Comments

Many of these seem to be even semiprimes.

Is this sequence infinite, and if so, can someone exhibit an explicitly calculable subsequence?

a(42) > 10^5, if it exists. - Amiram Eldar, May 02 2024

Crossrefs

Cf. A209312.

Programs

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := pracQ[n] = (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), ?(# > 1 &)]) == {}; q[n] := 2 == Sum[If[pracQ[p] && ((PrimeQ[n - p] && PrimeQ[n + p]) || (pracQ[n - p] && pracQ[n + p])), 1, 0], {p, 1, n - 1}]; Select[Range[4000], q] (* Amiram Eldar, May 02 2024 *)

Extensions

Data corrected by Amiram Eldar, May 02 2024