OFFSET
1,1
COMMENTS
The corresponding numbers of twin prime pairs divisors are 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, ...
The subsequence with two twin prime pairs is {420, 1050, 2310, 2730, 3360, 5880, 6090, 6300, 7350, 7560, 8820, 9240, 10500, 10710, 11550, 11970, 15330, 18060, 19380, 21840, 25410, 26250, 26880, 28350, 29400, ...}.
The subsequence with three twin prime pairs is interesting because we find a majority of symmetrical numbers of the form abcabc or abcabc0 (see A235716). The subsequence with three twin prime pairs is 180180, 270270, 300300, 330330, 390390, 420420, 474810, 540540, 660660, 755790, 840840, 1231230, 1261260, 1501500, 1510320, 1621620, 1699110, ...
The subsequence with four twin prime pairs is 106696590, 107987880, 232792560, 244120170, 300690390, 358888530, 432311880, 466936470, 601380780, 670770870, 766275510, 892371480, 978498570, 998887890, 999068070, ... [Michel Marcus, Jan 11 2014]
Apparently most terms are congruent to 0 mod 30. Terms that are not: 858, 9438, 21318, 40698, 60918, 64782, 69498, 70122, 99528, ... - Amiram Eldar, Aug 26 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
30 is in the sequence because the prime divisors are 2, 3, 5 and {3,5} is a twin primes.
420 is in the sequence because the prime divisors are 2, 3, 5, 7 => {3,5} and {5,7} are twin primes.
MAPLE
with(numtheory) :
for n from 1 to 3400 do:
p1:=ithprime(n):p2:=ithprime(n+1):
if p2=p1+2
then
ii:=0:x:=factorset(p1+1):n1:=nops(x):
for i from 1 to n1-1 do:
if x[i+1]=x[i]+2
then
ii:=ii+1:
else fi:
od:
if ii>0
then
printf(`%d, `, p1+1):
else fi:
fi:
od:
MATHEMATICA
Mean /@ Select[Split[Prime[Range[1000]], #2 - #1 == 2&], Length[#] == 2 && MemberQ[Differences[FactorInteger[Mean[#]][[All, 1]]], 2]&] (* Jean-François Alcover, Nov 06 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 11 2014
STATUS
approved