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A344843
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The smallest of three consecutive integers that are products of three or more primes.
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2
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98, 124, 152, 170, 174, 188, 230, 242, 243, 244, 284, 342, 343, 350, 368, 374, 404, 423, 424, 428, 434, 440, 474, 475, 494, 506, 530, 548, 574, 594, 602, 603, 604, 608, 636, 637, 638, 644, 650, 656, 663, 664, 710, 714, 724, 728, 740, 774, 775, 782, 804, 824
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OFFSET
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1,1
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LINKS
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EXAMPLE
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98 = 2*7*7, 99 = 3*3*11, 100 = 2*2*5*5. Three consecutive integers 98, 99, and 100 are each products of three or more primes. Thus, 98 is a term.
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MATHEMATICA
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Select[Range[1002], Total[Transpose[FactorInteger[#]][[2]]] >= 3 && Total[Transpose[FactorInteger[# + 1]][[2]]] >= 3 && Total[Transpose[FactorInteger[# + 2]][[2]]] >= 3 &]
p3pQ[k_]:=Boole[#>2&/@k]=={1, 1, 1}; Position[Partition[PrimeOmega[ Range[ 900]], 3, 1], _?p3pQ]//Flatten (* Harvey P. Dale, Nov 18 2021 *)
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PROG
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(PARI) is(n) = for(i = 0, 2, if(bigomega(n + i) < 3, return(0))); 1 \\ David A. Corneth, Jun 08 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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