A053319 Distance between the smaller members of successive twin prime pairs.

2, 6, 6, 12, 12, 18, 12, 30, 6, 30, 12, 30, 12, 6, 30, 12, 30, 12, 30, 36, 72, 12, 30, 60, 48, 30, 18, 24, 18, 150, 12, 6, 30, 24, 138, 12, 18, 12, 30, 60, 78, 48, 12, 12, 18, 108, 24, 30, 6, 120, 12, 48, 30, 24, 66, 84, 6, 54, 18, 48, 30, 54, 6, 24, 18, 12, 96, 30, 42, 30, 42

Offset: 1

Author

Labos Elemer, Mar 06 2000

Keywords

• nonn

Comments

Conjecture: a(n) < log(A014574(n))^3 for n > 2. - Thomas Ordowski, Jul 21 2012

This is of course also the distance between the larger members of successive twin primes. - Franklin T. Adams-Watters, Jun 03 2014

Links

• M. F. Hasler, Table of n, a(n) for n = 1..107406

Crossrefs

First differences of A001359, A006512, and of A014574.

Programs

Mathematica

Differences[Transpose[Select[Partition[Prime[Range[450]],2,1],Last[#]-First[#]==2&]][[1]]]  (* Harvey P. Dale, Feb 08 2011 *)

PARI

{cnt=0; lp= /*last*/ ltp=/*last twin(upper)*/ 5;
forprime(p=lp+1,default(primelimit), if(p-lp != 2,lp=p;next);
write("b053319.txt",cnt++" "p-ltp);/* print1(p-ltp", ");*/ ltp=lp=p)} \\ M. F. Hasler, May 26 2007

Extensions

Definition clarified by Harvey P. Dale, Feb 08 2011