A088711 - OEIS

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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.

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