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A286195 Products of two numbers that are the average of a pair of twin primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A014613 A046370 A103248 * A140135 A120142 A110228

Adjacent sequences:  A286192 A286193 A286194 * A286196 A286197 A286198

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 12 2017

STATUS

approved

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Last modified October 15 04:45 EDT 2018. Contains 316200 sequences. (Running on oeis4.)