A286195 Products of two numbers that are the average of a pair of twin primes.

16, 24, 36, 48, 72, 108, 120, 144, 168, 180, 216, 240, 252, 288, 324, 360, 408, 432, 504, 540, 552, 600, 612, 648, 720, 756, 768, 792, 828, 864, 900, 912, 960, 1080, 1128, 1152, 1188, 1224, 1248, 1260, 1296, 1368, 1392, 1440, 1620, 1656, 1680, 1692, 1728, 1764, 1800

Offset

1,1

Comments

Product of two numbers from A014574 in at least one way. - David A. Corneth, Jun 12 2017

For n > 1, a(n) is divisible by 12. All terms not in 4*A014574 are divisible by 36. - Robert Israel, Jun 12 2017

A075369 Union A288639.

Links

Vincenzo Librandi and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1182 terms from Vincenzo Librandi)

Example

4 and 12 are the average of twin prime pairs (i.e., 4 = (3+5)/2 and 12 = (11+13)/2) and 4*12 = 48, which is in the sequence.
As 4 is the average of a twin prime pair, 4*4 = 16 is also in the sequence. - David A. Corneth, Jun 12 2017

Maple

N:= 2000: # to get all terms <= N
P:= select(isprime, {seq(i, i=3..N/4+1, 2)}):
B:= map(`+`, P, 1) intersect map(`-`, P, 1):
sort(convert(select(`<=`, {seq(seq(B[i]*B[j], j=1..i), i=1..nops(B))}, N), list));
# Robert Israel, Jun 12 2017

Mathematica

With[{nn = 1800}, TakeWhile[Union@ Map[Times @@ # &, Tuples[#, {2}]], # <= nn &] &@ Map[Mean, Select[Partition[Prime@ Range@ PrimePi@ nn, 2, 1], Differences@ # == {2} &]]] (* Michael De Vlieger, Jun 12 2017 *)

Prog

(PARI) upto(n) = {my(l1=List(), l2=List(), p, q);
p=2; forprime(q=3, n, if(q-p==2, listput(l1, p+1)); p=q); for(i=1, #l1, for(j=i, #l1, if(l1[i]*l1[j]<=n, listput(l2, l1[i]*l1[j]), next(2)))); listsort(l2, 1); l2} \\ prog adapted from PARI-prog from Charles R Greathouse IV in A014574. - David A. Corneth, Jun 12 2017

Crossrefs

Cf. A014574, A249628, A288639.

A075369 is a subsequence.

Sequence in context: A046370 A376704 A103248 * A140135 A349241 A120142

Adjacent sequences: A286192 A286193 A286194 * A286196 A286197 A286198

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2017

Status

approved