A219556 Semiprimes neighboring a 3-smooth number.

4, 9, 10, 15, 17, 25, 26, 28, 33, 35, 37, 49, 55, 65, 82, 95, 97, 129, 143, 145, 161, 163, 215, 217, 287, 289, 323, 325, 485, 487, 511, 513, 649, 767, 769, 865, 973, 1457, 1459, 1535, 1537, 1727, 1729, 1943, 1945, 2047, 2049, 2186, 2188, 2305, 3071, 3073, 3455, 3457

Offset: 1

Author

Jonathan Vos Post, Nov 22 2012

Keywords

• nonn
• easy

Comments

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

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

Examples

			a(1) = (2^0)*(3^1) + 1 = (2^2)*(3^0) - 1 = 4 = 2*2, a semiprime.
a(2) = (2^3)*(3^0) + 1 = 9 = 3*3.
a(3) = (2^0)*(3^2) + 1 = 10 = 2*5.
a(4) = (2^4)*(3^0) - 1 = 15 = 3*5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4377 (terms below 10^60)

Crossrefs

Cf. A001358, A003586, A219528.

Programs

Mathematica

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 *)