A067814 The start of a record-breaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 4.

16, 135, 1274, 4023, 12122, 204323, 355923, 3405122, 49799889, 202536181, 3195380868, 5208143601, 85843948321, 97524222465

Offset: 1

Author

Shyam Sunder Gupta, Feb 07 2002

Keywords

• fini
• full
• nonn

Comments

3405122 is the first number having 8 and 9 consecutive integers with 4 prime factors. - T. D. Noe, Mar 19 2014

Examples

			a(4)=4023 because 4023 is the start of a record breaking run of 4 consecutive integers (4023 to 4026) each having 4 prime factors; i.e. bigomega(n)=A001222(n)=4 for n = 4023, ..., 4026.
		

Crossrefs

Cf. A067813, A067820, A067821, A067822.

Programs

Mathematica

bigomega[n_] := Plus@@Last/@FactorInteger[n]; For[n=1; m=l=0, True, n++, If[bigomega[n]==4, l++, If[l>m, m=l; Print[n-l, " ", l]]; l=0]]

Extensions

Edited by Dean Hickerson, Jul 31 2002

More terms from Don Reble, Aug 11 2002, who remarks that the sequence is now complete.