

A087641


Start of the first sequence of exactly n consecutive pairs of twin primes.


13



29, 101, 5, 9419, 909287, 325267931, 678771479, 1107819732821, 170669145704411, 3324648277099157, 789795449254776509
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Start of the smallest twin prime clusters of order n such that the following and preceding two primes must be neither twin primes between themselves nor with the ends of the string.  Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 22 2006
Sequences of n consecutive pairs of twin primes are called twin prime clusters of order n. Here (and in the sequences A035789, ..., A035795) it is requested that the order be exactly n, i.e., the preceding prime and the following prime must not be (upper resp. smaller) member of another twin prime pair. Note that a(3)=5 is preceded by 3 which is member of the twin prime pair (3,5) but not upper member of a preceding twin prime pair. Since it cannot happen elsewhere that P2=P32 if P3=P42 (using notations of A179067 and A035791), there is no condition imposed on P3P2, and the condition on P2P1 is also satisfied for P3=5. This sequence lists the starting prime of the cluster corresponding to the first occurrence of n in A179067.  M. F. Hasler, May 04 2015


LINKS

Table of n, a(n) for n=1..11.
Hugo Pfoertner, Consecutive pairs of twin primes. FORTRAN program.
Carlos Rivera, Puzzle 122. Consecutive Twin primes, The Prime Puzzles and Problems Connection.
Eric Weisstein's World of Mathematics, Twin Prime Cluster


EXAMPLE

a(6)=325267931 is the starting point of the first occurrence of 6 consecutive pairs of twin primes: (325267931 325267933) (325267937 325267939) (325267949 325267951) (325267961 325267963) (325267979 325267981) (325267991 325267993).


CROSSREFS

Cf. A001359, A111950.
The sequence consists of the initial terms of A035789, A035790, A035791, A035792, A035793, A035794, A035795, A263205, A259034.
Sequence in context: A154405 A092373 A240954 * A161665 A127464 A318959
Adjacent sequences: A087638 A087639 A087640 * A087642 A087643 A087644


KEYWORD

more,nonn


AUTHOR

Hugo Pfoertner, Sep 15 2003


EXTENSIONS

Extended by Jud McCranie
a(8)a(10) from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 22 2006
a(11) found by Gabor Levai in October 2011 (see Rivera), added by Dmitry Kamenetsky, Dec 15 2018


STATUS

approved



