A109875 Chen primes p such that their p + 2 counterpart is a golden semiprime.

13, 587, 1361, 15227, 118967, 337721, 383267, 512891, 1027331, 1780151, 2303681, 8200391, 9310517, 14666579, 25005089, 29105981, 34824971, 38895497, 40436909, 51819461, 63462977, 65427749, 65599199, 66043091, 75552479, 94671671

Offset

1,1

Comments

Conjecture: sequence is infinite.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1361 is a term because it is prime and 1363 = 29*47 and abs(29*phi - 47) = 0.07701... < 1.

Mathematica

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p = 1; Do[p = NextPrime[p]; q = f[p]; If[q > 0 && PrimeQ[p*q - 2], AppendTo[seq, p*q - 2]], {1000}]; seq (* Amiram Eldar, Nov 29 2019 *)

Crossrefs

Cf. A109611, A108540.

Sequence in context: A076461 A168601 A142210 * A258303 A275045 A296951

Adjacent sequences: A109872 A109873 A109874 * A109876 A109877 A109878

Keyword

nonn

Author

Jason Earls, Aug 31 2005

Extensions

a(15)-a(26) from Donovan Johnson, Nov 17 2008

Status

approved