

A109875


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


1



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



