login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A256617 Numbers having exactly two distinct prime factors, which are also adjacent prime numbers. 15
6, 12, 15, 18, 24, 35, 36, 45, 48, 54, 72, 75, 77, 96, 108, 135, 143, 144, 162, 175, 192, 216, 221, 225, 245, 288, 323, 324, 375, 384, 405, 432, 437, 486, 539, 576, 648, 667, 675, 768, 847, 864, 875, 899, 972, 1125, 1147, 1152, 1215, 1225, 1296, 1458, 1517, 1536, 1573, 1715, 1728, 1763, 1859, 1875, 1944 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A001222(a(n)) = 2;

A006530(a(n)) = A151800(A020639(n)) = A000040(A049084(A020639(a(n)))+1).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

.   n | a(n)                      n | a(n)

. ----+------------------       ----+------------------

.   1 |   6 = 2 * 3              13 |  77 = 7 * 11

.   2 |  12 = 2^2 * 3            14 |  96 = 2^5 * 3

.   3 |  15 = 3 * 5              15 | 108 = 2^2 * 3^3

.   4 |  18 = 2 * 3^2            16 | 135 = 3^3 * 5

.   5 |  24 = 2^3 * 3            17 | 143 = 11 * 13

.   6 |  35 = 5 * 7              18 | 144 = 2^4 * 3^2

.   7 |  36 = 2^2 * 3^2          19 | 162 = 2 * 3^4

.   8 |  45 = 3^2 * 5            20 | 175 = 5^2 * 7

.   9 |  48 = 2^4 * 3            21 | 192 = 2^6 * 3

.  10 |  54 = 2 * 3^3            22 | 216 = 2^3 * 3^3

.  11 |  72 = 2^3 * 3^2          23 | 221 = 13 * 17

.  12 |  75 = 3 * 5^2            24 | 225 = 3^2 * 5^2 .

MATHEMATICA

Select[Range[2000], MatchQ[FactorInteger[#], {{p_, _}, {q_, _}} /; q == NextPrime[p]]&] (* Jean-François Alcover, Dec 31 2017 *)

PROG

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a256617 n = a256617_list !! (n-1)

a256617_list = f (singleton (6, 2, 3)) $ tail a000040_list where

   f s ps@(p : ps'@(p':_))

     | m < p * p' = m : f (insert (m * q, q, q')

                          (insert (m * q', q, q') s')) ps

     | otherwise  = f (insert (p * p', p, p') s) ps'

     where ((m, q, q'), s') = deleteFindMin s

(PARI) is(n) = if(omega(n)!=2, return(0), my(f=factor(n)[, 1]~); if(f[2]==nextprime(f[1]+1), return(1))); 0 \\ Felix Fröhlich, Dec 31 2017

(PARI) list(lim)=my(v=List(), c=sqrtnint(lim\=1, 3), d=nextprime(c+1), p=2); forprime(q=3, d, for(i=1, logint(lim\q, p), my(t=p^i); while((t*=q)<=lim, listput(v, t))); p=q); forprime(q=d+1, lim\precprime(sqrtint(lim)), listput(v, p*q); p=q); Set(v) \\ Charles R Greathouse IV, Apr 12 2020

CROSSREFS

Subsequence of A007774, subsequences: A006094, A033845, A033849, A033851.

Cf. A000040, A001222, A020639, A006530, A049084, A151800.

Sequence in context: A309944 A212308 A089341 * A252044 A315617 A287572

Adjacent sequences:  A256614 A256615 A256616 * A256618 A256619 A256620

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 05 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 15:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)