A219556 - OEIS

%I #17 Jul 13 2023 01:52:41

%S 4,9,10,15,17,25,26,28,33,35,37,49,55,65,82,95,97,129,143,145,161,163,

%T 215,217,287,289,323,325,485,487,511,513,649,767,769,865,973,1457,

%U 1459,1535,1537,1727,1729,1943,1945,2047,2049,2186,2188,2305,3071,3073,3455,3457

%N Semiprimes neighboring a 3-smooth number.

%C This is to A219528 as semiprime A001358 are to primes A000040.

%C Semiprime numbers of the form of 2^j*3^k +/- 1.

%H Amiram Eldar, <a href="/A219556/b219556.txt">Table of n, a(n) for n = 1..4377</a> (terms below 10^60)

%e a(1) = (2^0)*(3^1) + 1 = (2^2)*(3^0) - 1 = 4 = 2*2, a semiprime.

%e a(2) = (2^3)*(3^0) + 1 = 9 = 3*3.

%e a(3) = (2^0)*(3^2) + 1 = 10 = 2*5.

%e a(4) = (2^4)*(3^0) - 1 = 15 = 3*5.

%t mx = 4000; A003586 = Flatten@ Table[2^i*3^j, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx/2^i]}]; Union@ Join[ Select[A003586, PrimeOmega[# - 1] == 2 &] - 1, Select[A003586, PrimeOmega[# - 1] == 2 || PrimeOmega[# + 1] == 2 &] + 1] (* _Robert G. Wilson v_, Nov 22 2012 *)

%Y Cf. A001358, A003586, A219528.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Nov 22 2012