

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(qp==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 PARIprog 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



