A235483 Average of twin prime pairs that contains at least one twin prime pair as divisors.

30, 60, 150, 180, 240, 270, 420, 570, 600, 660, 810, 858, 1020, 1050, 1230, 1290, 1320, 1620, 1950, 2130, 2310, 2340, 2550, 2730, 2790, 2970, 3000, 3120, 3300, 3330, 3360, 3390, 3540, 3930, 4020, 4050, 4230, 4260, 4650, 4800, 5010, 5100, 5280, 5520, 5640, 5850

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

Cf. A001097, A014574, A235716.

Sequence in context: A143207 A359410 A108454 * A064783 A228877 A258879

Adjacent sequences: A235480 A235481 A235482 * A235484 A235485 A235486

Keyword

nonn

Author

Michel Lagneau, Jan 11 2014

Status

approved