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 A242805 Integers n such that each of n,n+1,n+2,n+4,n+5,n+6 is the squarefree product of three primes. 5
 73293, 120237, 122613, 130429, 143493, 147953, 171893, 180965, 199833, 213153, 219201, 268017, 287493, 298433, 299553, 300093, 313701, 329793, 332889, 341781, 363597, 369393, 376201, 392509, 404453, 432393, 460801, 475809, 493597, 503457, 506517, 508677 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is remarkable that this sequence starts with considerably bigger density than the analog A242804 for squarefree integers with two prime divisors. The exceptional density causes the problem that overlapping sextets appear very soon and rather frequently, whereas in A242804 the phenomenon of overlapping sextets does not occur up to the bound 9*10^9. In fact, there exist 114 nonets n,n+1,n+2,n+4,n+5,n+6,n+8,n+9,n+10 of squarefree integers with exactly three prime divisors, up to 10^8. The PARI script in PROG does not start a new sextet before the previous sextet was completed. The impact on bigger clusters, such as nonets and dodekuplets, is illustrated in the CAVEAT of section EXAMPLE. LINKS Zak Seidov, Table of n, a(n) for n = 1..176 EXAMPLE 73293=3*11*2221, 73294=2*13*2819, 73295=5*107*137, 73297=7*37*283, 73298=2*67*547, 73299=3*53*461; CAVEAT: (1) For the dodekuplet, which starts together with the first nonet, 969833=17*89*641, 969834=2*3*161639, 969835=5*31*6257, 969837=3*11*29389, 969838=2*173*2803, 969839=13*61*1223, 969841=23*149*283, 969842=2*59*8219, 969843=3*7*46183, 969845=5*47*4127, 969846=2*3*161641, 969847 =29*53*631, the PARI script lists 969833 and 969841, but not 969837; (2) For the second nonet, 1450257=3*229*2111, 1450258=2*179*4051, 1450259=83*101*173, 1450261=29*43*1163, 1450262=2*11*65921, 1450263=3*191*2531, 1450265=5*23*12611, 1450266=2*3*241711, 1450267=7*13*15937, the PARI script lists 1450257 only, but not 1450261. MATHEMATICA s = {}; Do[If[AllTrue[{k, k + 1, k + 2, k + 4, k + 5, k + 6}, SquareFreeQ] && {3, 3, 3, 3, 3, 3} == PrimeOmega[{k, k + 1, k + 2, k + 4, k + 5, k + 6}], AppendTo[s, k]], {k, 73293, 2000000, 4}]; s (* Zak Seidov, Nov 12 2018 *) PROG (PARI) { default(primelimit, 1000M); i=0; j=0; k=0; l=0; m=0; loc=0; lb=2; ub=9*10^9; o=3; for(n=lb, ub, if(issquarefree(n)&&(o==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1

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Last modified November 19 08:48 EST 2018. Contains 317347 sequences. (Running on oeis4.)