A088708 Numbers n which are a product of two primes j and k such that n+j-k and n-j+k are both primes.

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

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+7-31 and 217-7+31 (193 and 241) are primes.

Mathematica

pdpQ[{a_, b_}]:=Module[{d=b-a}, 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