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A136358 Increasing sequence obtained by union of two sequences {b(n)} and {c(n)}, where b(n) is the smallest odd composite number m such that both m-2 and m+2 are prime and the set of distinct prime factors of m consists of the first n odd primes and c(n) is the smallest composite number m such that both m-1 and m+1 are primes and the set of the distinct prime factors of m consists of the first n primes. 6
4, 6, 9, 15, 30, 105, 420, 2310, 3465, 15015, 180180, 765765, 4084080, 106696590, 247342095, 892371480, 3011753745, 9704539845, 100280245065, 103515091680, 4412330782860, 29682952539240, 634473110526255, 22514519501013540 (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(1)=4 is preceded by 3 and followed by 5, both primes; a(3)=9, preceded by 7 and followed by 11, both primes.

MATHEMATICA

b[n_]:=(d=Product[Prime[k], {k, n}]; For[m=1, !(!PrimeQ[d*m]&&PrimeQ[d*m-1] &&PrimeQ[d*m+1]&&Length[FactorInteger[c*m]]==n), m++ ]; d*m); c[n_]:=(d=Product [Prime[k], {k, 2, n+1}]; For[m=1, !(!PrimeQ[d*(2*m-1)]&&PrimeQ[d(2m-1)-2]&&PrimeQ [d(2m-1)+2]&&Length[FactorInteger[d(2m-1)]]==n), m++ ]; d(2m-1)); Take[Union[Table [b[k], {k, 24}], Table[c[k], {k, 24}]], 24] (* Farideh Firoozbakht, Aug 13 2009 *)

PROG

(UBASIC)

10 'A136358, Enoch Haga, Jun 19 2009'

11 'compute and combine input 2 or 3 separately; begin with 4 and 9

20 input "prime, 2 or 3"; A

30 if A=2 or A=3 then B=nxtprm(A)

40 print A; B; :R=A*B:print R; :stop

50 if even(R)=1 then if R-1=prmdiv(R-1) and R+1=prmdiv(R+1) then print "*"

60 if even(R)=0 then if R-2=prmdiv(R-2) and R+2=prmdiv(R+2) then print "+"

61 print R:stop

70 B=nxtprm(B):R=B*R

90 print B; R:stop

100 goto 50

- Enoch Haga, Jul 11 2009

CROSSREFS

Cf. A136349-A136357, A070826, A118750.

Sequence in context: A065856 A136357 A136356 * A115665 A118694 A085648

Adjacent sequences:  A136355 A136356 A136357 * A136359 A136360 A136361

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 February 23 15:00 EST 2020. Contains 332166 sequences. (Running on oeis4.)