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
Keywords
Examples
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
Links
- Vincenzo Librandi and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1182 terms from Vincenzo Librandi)
Programs
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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 *) -
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
Comments