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A088711 Numbers n that are a product of two primes j and k such that both n+j+k and n-j-k are primes. 1
10, 14, 15, 21, 26, 33, 35, 38, 51, 65, 86, 93, 111, 123, 161, 201, 203, 206, 209, 215, 221, 278, 321, 371, 395, 398, 413, 471, 485, 533, 543, 545, 551, 626, 671, 698, 723, 755, 779, 803, 815, 866, 905, 993, 1046, 1286, 1349, 1371, 1383, 1385, 1403, 1461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Zak Seidov, Table of n, a(n) for n=1..1616, a(n)<200000

EXAMPLE

a(1)=10 because 10 has only one pair of prime factors (2 and 5) and both 10+2+5 and 10-2-5 (17 and 3) are primes.

MATHEMATICA

a[n_]:={1, 1}==Last/@FactorInteger[n]; b[n_]:=First[First/@FactorInteger[n]]+Last[First/@FactorInteger[n]]; Select[Range[6, 3000], a[#]&&PrimeQ[#-b[#]]&&PrimeQ[#+b[#]]&] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *)

Reap[Do[fi=FactorInteger[n]; la=Last/@fi; If[{1, 1}==la, pq=fi[[1, 1]]+fi[[2, 1]]; If[PrimeQ[n-pq] && PrimeQ[n+pq], Sow[n]]], {n, 6, 200000}]][[2, 1]] (* used to create b-file, Zak Seidov, Mar 04 2011 *)

CROSSREFS

Cf. A001358, A088709, A088710.

Sequence in context: A235690 A271568 A229271 * A154774 A162708 A330210

Adjacent sequences:  A088708 A088709 A088710 * A088712 A088713 A088714

KEYWORD

nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 11 2003

STATUS

approved

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Last modified June 18 09:17 EDT 2021. Contains 345098 sequences. (Running on oeis4.)