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A242605
Start of a triple of consecutive squarefree numbers which are all semiprimes.
6
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.
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 18 2014
STATUS
approved