A213606 Greater of a pair (x,y) of consecutive terms of A045572 which are both semiprimes and such that the prime factors of x are adjacent primes to the factors of y.

407, 1007, 110207, 118007, 418309, 429493, 439099, 559007, 1239871, 1887241, 2481467, 2502979, 3381407, 3693421, 5646259, 6120407, 6586007, 6954769, 7042663, 8350007, 11305097, 13083407, 13760207, 17297521, 21159421

Offset: 1

Author

M. F. Hasler, Jun 15 2012

Keywords

• nonn

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).

Examples

			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.
		

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.

Crossrefs

Cf. A213605 (the lesser ("x") of the pair of semiprimes).