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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

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) = 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.

CROSSREFS

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

Sequence in context: A128767 A097740 A325151 * A083815 A250893 A261857

Adjacent sequences:  A213602 A213603 A213604 * A213606 A213607 A213608

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jun 15 2012

STATUS

approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)