

A213605


Lesser of a pair (x,y) of consecutive terms of A045572 (numbers coprime to 2*5), both semiprimes and such that the prime factors of x are adjacent primes to the factors of y.


2



403, 1003, 110203, 118003, 418307, 429491, 439097, 559003, 1239869, 1887239, 2481463, 2502977, 3381403, 3693419, 5646257, 6120403, 6586003, 6954767, 7042661, 8350003, 11305093, 13083403, 13760203, 17297519, 21159419
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Within the subset A045572 of numbers ending in 1, 3, 7 or 9, i.e., excluding numbers having 2 or 5 as prime factor, we look for two consecutive elements (x,y) which are both semiprimes and whose prime factors are "adjacent" primes, i.e., if x=p(i)*p(j), then we require y=p(i +/ 1)*p(j +/ 1).


LINKS

Table of n, a(n) for n=1..25.
Woodhodgson, Adjacent composite numbers with pairs of adjacent prime factors, Primenumbers Group, Jun 15 2012.
Woodhodgson, Maximilian Hasler, Adjacent composite numbers with pairs of adjacent prime factors, digest of 2 messages in primenumbers Yahoo group, Jun 14  Jun 15, 2012.


EXAMPLE

a(1) = 403 because (403,407) are such that 403=13*31 and 407=11*37, (11,13) and (31,37) being consecutive primes.
a(2) = 1003 because (1003,1007) are such that 1003=17*59 and 1007=19*53, where (17,19) and (53,59) are pairs of subsequent primes.


CROSSREFS

Cf. A213606 (the greater ("y") of the pair of semiprimes).
Sequence in context: A128767 A097740 A325151 * A083815 A250893 A261857
Adjacent sequences: A213602 A213603 A213604 * A213606 A213607 A213608


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jun 15 2012


STATUS

approved



