A383400 Starting values of maximal runs of at least five integers, each with exactly two distinct prime factors.
54, 91, 115, 141, 158, 205, 212, 295, 301, 323, 391, 535, 685, 721, 799, 1135, 1345, 1465, 1535, 1711, 1941, 1981, 2101, 2215, 2302, 2425, 2641, 3865, 4411, 5461, 6505, 6625, 6925, 7165, 7231, 7261, 7441, 7855, 7891, 8575, 9121, 9355, 9571
Offset: 1
Keywords
Examples
a(1) = 54 (run length 5) 53 = 53: omega = 1 (prime, so the previous number is not counted) 54 = 2 * 3^3: omega = 2 55 = 5 * 11: omega = 2 56 = 2^3 * 7: omega = 2 57 = 3 * 19: omega = 2 58 = 2 * 29: omega = 2 (58 is the last member; 59 is prime) a(2) = 91 (run length 6) 90 = 2 * 3^2 * 5: omega = 3 91 = 7 * 13: omega = 2 92 = 2^2 * 23: omega = 2 93 = 3 * 31: omega = 2 94 = 2 * 47: omega = 2 95 = 5 * 19: omega = 2 96 = 2^5 * 3: omega = 2 (97 is prime, so the run stops at 96) a(4) = 141 (run length 8) 140 = 2^2 * 5 * 7: omega = 3 141 = 3 * 47: omega = 2 142 = 2 * 71: omega = 2 143 = 11 * 13: omega = 2 144 = 2^4 * 3^2: omega = 2 145 = 5 * 29: omega = 2 146 = 2 * 73: omega = 2 147 = 3 * 7^2: omega = 2 148 = 2^2 * 37: omega = 2 (149 is prime)
Programs
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Mathematica
With[{s = Select[Range[10000], PrimeNu[#] == 2 &]}, First /@ Select[Split[s, #2 == #1 + 1 &], Length[#] >= 5 &] ]
Comments