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!)
A135257 Smallest semiprimes such that a(j) - a(k) are all different. 1
4, 6, 9, 10, 21, 34, 55, 65, 74, 94, 141, 177, 203, 219, 298, 321, 395, 403, 529, 581, 635, 662, 731, 934, 982, 1073, 1145, 1317, 1418, 1762, 1769, 1849, 1915, 2066, 2165, 2305, 2327, 2746, 2809, 3127, 3409, 3859, 3983, 4138, 4285, 4559, 4742, 5186, 5299, 5854 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Semiprime analog of A079848. This is the slowest-growing semiprime B2 sequence (see A005282). The difference set through a(n) must have cardinality exactly C(n,2) = n*(n+1)/2 = A000217(n-1).

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(1) = 4, the smallest semiprime (A001358(1)).

a(2) = 6 = A001358(2); the difference set so far is {2}.

a(3) = 9 = A001358(3); the difference set so far is {2,3,5}.

a(4) = 10 = A001358(4); the difference set so far is {1,2,3,4,5,6}.

a(5) can't be 14 = A001358(5) because 14-10 =4, in the difference set through a(4); can't be 15 = A001358(6) because 15-10 =5, in the difference set through a(4)...

a(5) = 21 = A001358(7); the difference set so far is {1,2,3,4,5,6,11,12,15,17}.

a(6) = 34 = A001358(12); the difference set so far is {1,2,3,4,5,6,11,12,13,15,17,24,25,28,30}.

MAPLE

A135257 := proc(nmax) local a, anext, diffset, good, an ; a := [4, 6] ; diffset := {2} ; while nops(a) < nmax do for anext from op(-1, a)+1 do if numtheory[bigomega](anext) = 2 then good := true ; for an in a do if ( anext-an) in diffset then good := false ; break ; fi ; od; if good then for an from 1 to nops(a) do diffset := diffset union { anext-op(an, a) } ; od; a := [op(a), anext] ; break ; fi ; fi ; od ; od: a ; end: A135257(60) ; # R. J. Mathar, Jan 08 2008

CROSSREFS

Cf. A000217, A001358, A005282, A079848.

Sequence in context: A118778 A108635 A071964 * A118697 A118695 A235108

Adjacent sequences:  A135254 A135255 A135256 * A135258 A135259 A135260

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Dec 01 2007

EXTENSIONS

Corrected and extended by R. J. Mathar, Jan 08 2008

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 May 28 04:36 EDT 2020. Contains 334671 sequences. (Running on oeis4.)