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A136357 Increasing sequence obtained by union of two sequences A136354 and {b(n)}, where b(n) is the smallest composite number m such that m+1 is prime and the set of distinct prime factors of m consists of the first n primes. 3
4, 6, 9, 15, 30, 105, 210, 2310, 3465, 15015, 120120, 765765, 4084080, 33948915, 106696590, 334639305, 892371480, 3234846615, 71166625530, 100280245065, 200560490130, 3710369067405, 29682952539240, 1369126185872445 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is different from A070826 and A118750.

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

a(4)=15 because k=2 with prime factors 3 and 5 and 15 is followed by 17, prime;

a(5)=30 because k=3 with prime factors 2, 3, 5 and 30 is followed by 31, prime.

MATHEMATICA

a[n_]:=(c=Product[Prime[k], {k, n}]; For[m=1, !(!PrimeQ[c*m]&&PrimeQ[c*m+1]&& Length[FactorInteger[c*m]]==n), m++ ]; c*m);

b[n_]:=(c=Product[Prime[k], {k, 2, n+1}]; For[m=1, !(!PrimeQ[c(2*m-1)]&&PrimeQ[c(2*m-1)+2]&&Length[FactorInteger [c(2*m-1)]]==n), m++ ]; c(2*m-1));

Take[Union[Table[a[k], {k, 24}], Table[b[k], {k, 24}]], 24] (* Farideh Firoozbakht, Aug 13 2009 *)

CROSSREFS

Cf. A136349-A136356, A136358, A070826, A118750.

Sequence in context: A183978 A118696 A065856 * A136356 A136358 A115665

Adjacent sequences:  A136354 A136355 A136356 * A136358 A136359 A136360

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Dec 25 2007

EXTENSIONS

Edited, corrected and extended by Farideh Firoozbakht, Aug 13 2009

STATUS

approved

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Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)