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

1,1

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

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) = 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

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

Sequence in context: A172921 A063138 A118327 * A343157 A063145 A281859

Adjacent sequences: A213603 A213604 A213605 * A213607 A213608 A213609

Keyword

nonn

Author

M. F. Hasler, Jun 15 2012

Status

approved