OFFSET
1,1
COMMENTS
Within the sequence 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
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) = 407 is the second member of the pair (403,407) which is such that 403=13*31 and 407=11*37, (11,13) and (31,37) being pairs of consecutive primes. This is the smallest pair having these properties.
a(2) = 1007 because (1003,1007) is the second smallest pair of consecutive numbers among those ending in 1,3,7 or 9, which are both semiprimes and such that 1003=17*59 and 1007=19*53, where (17,19) and (53,59) are pairs of consecutive primes.
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jun 15 2012
STATUS
approved