A242605 Start of a triple of consecutive squarefree numbers which are all semiprimes.

33, 55, 85, 91, 93, 115, 118, 119, 141, 142, 143, 158, 201, 202, 203, 205, 213, 214, 215, 217, 218, 295, 298, 299, 301, 302, 323, 326, 391, 393, 411, 413, 445, 451, 511, 514, 535, 542, 551, 622, 633, 685, 694, 695, 697, 745, 763, 778, 791, 799, 815, 842, 843, 865, 898, 921, 922

Offset

1,1

Comments

Sequence A039833 is a subsequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Daniel C. Mayer, Define an "m-triple" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors, Number Theory group on LinkedIn.com

Example

33 is in the sequence because 33, 34, 35 are all squarefree semiprimes.
55 is in the sequence because 55, 57, 58 (we ignore 56 because it's not squarefree) are all squarefree semiprimes.

Mathematica

Transpose[Select[Partition[Select[Range[1000], SquareFreeQ], 3, 1], Union[ PrimeOmega[ #]] =={2}&]][[1]] (* Harvey P. Dale, Feb 07 2016 *)

Prog

(PARI) is_A242605(n, c=2)==issquarefree(n)&&omega(n)==2&&(!c||until(issquarefree(n++), )||is_A242605(n, c-1))
(PARI) (back(n, c=1)=until(issquarefree(n--)&&c--, ); n); for(n=1, 999, issquarefree(n)||next; dk==4&&dk==dm&&numdiv(n)==dm&&print1(back(n)", "); dk=dm; dm=numdiv(n))

Crossrefs

Cf. A242606 (m=3), A242607 (m=4), A242608 (m=5), A242621 (first terms for positive m).

Sequence in context: A061864 A075810 A132288 * A351396 A350598 A260872

Adjacent sequences: A242602 A242603 A242604 * A242606 A242607 A242608

Keyword

nonn

Author

M. F. Hasler, May 18 2014

Status

approved