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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 12:53 EST 2021. Contains 349419 sequences. (Running on oeis4.)