A101294 - OEIS

%I #11 May 16 2017 04:30:35

%S 56,93,94,117,143,144,145,146,160,207,214,215,216,217,297,303,325,326,

%T 327,393,537,687,723,801,1137,1347,1467,1537,1713,1943,1983,2103,2217,

%U 2304,2305,2306,2427,2643,2666,2716,3867,3914,4413

%N Numbers n such that omega(n-2) = omega(n-1) = omega(n) = omega(n+1) = omega(n+2).

%H G. C. Greubel, <a href="/A101294/b101294.txt">Table of n, a(n) for n = 1..5000</a>

%e 143 is in the sequence because it has two unique prime factors (11 and 13), the same number as its two nearest neighbors on both sides (141 has 3 and 47, 142 has 2 and 71, 144 has 2 and 3 and 145 has 5 and 29).

%t For[i=2, i<10000, If[And[Length[FactorInteger[i-2]]==Length[FactorInteger[i]], Length[FactorInteger[i-1]]==Length[FactorInteger[i]], Length[FactorInteger[i+1]]==Length[FactorInteger[i]], Length[FactorInteger[i+2]]==Length[FactorInteger[i]]], Print[i]];i++ ]

%t Select[Range[600000], PrimeNu[# - 2] == PrimeNu[# - 1] == PrimeNu[#] == PrimeNu[# + 1] == PrimeNu[# + 2] &] (* _G. C. Greubel_, May 15 2017 *)

%Y Cf. A001221, A101932.

%K easy,nonn

%O 1,1

%A _Neil Fernandez_, Dec 21 2004

%E Edited by _N. J. A. Sloane_, Mar 17 2007