A344843 The smallest of three consecutive integers that are products of three or more primes.

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

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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 *)

Prog

(PARI) is(n) = for(i = 0, 2, if(bigomega(n + i) < 3, return(0))); 1 \\ David A. Corneth, Jun 08 2021

Crossrefs

Sequence in context: A039491 A283555 A244207 * A109553 A268253 A105405

Adjacent sequences: A344840 A344841 A344842 * A344844 A344845 A344846

Keyword

nonn

Author

Tanya Khovanova, Jun 07 2021

Status

approved