

A088708


Numbers n which are a product of two primes j and k such that n+jk and nj+k are both primes.


5



6, 10, 15, 22, 57, 85, 87, 142, 187, 217, 235, 267, 274, 295, 339, 382, 505, 565, 579, 589, 667, 694, 799, 835, 849, 862, 889, 922, 1059, 1111, 1159, 1317, 1339, 1555, 1569, 1797, 1969, 1977, 2122, 2182, 2217, 2227, 2229, 2245, 2319, 2335, 2359, 2497, 2577
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OFFSET

1,1


COMMENTS

In other words, numbers n which are a product of two distinct primes a and b such that n+d are primes, where d is the difference between a and b.


LINKS

Table of n, a(n) for n=1..49.


EXAMPLE

a(10)=217 because 217 has only one pair of prime factors (7 and 31) and both 217+731 and 2177+31 (193 and 241) are primes.


MATHEMATICA

pdpQ[{a_, b_}]:=Module[{d=ba}, AllTrue[a*b+{d, d}, PrimeQ]]; With[{upto = 2600}, Select[ Times@@@Select[Subsets[Prime[Range[upto/2]], {2}], pdpQ]// Union, #<=upto&]] (* Harvey P. Dale, Aug 02 2016 *)


CROSSREFS

Cf. A001358.
Sequence in context: A157344 A332765 A093773 * A174872 A229273 A315285
Adjacent sequences: A088705 A088706 A088707 * A088709 A088710 A088711


KEYWORD

nonn


AUTHOR

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


STATUS

approved



