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.

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

Offset: 1

Author

M. F. Hasler, Jun 15 2012

Keywords

• nonn

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).

Examples

			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.
		

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. A213606 (the greater ("y") of the pair of semiprimes).