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

Author

M. F. Hasler, May 18 2014

Keywords

• nonn

Comments

Sequence A039833 is a subsequence.

Examples

			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.
		

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

Crossrefs

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

Programs

Mathematica

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

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))