A109875 - OEIS

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

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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