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

1,1

Comments

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

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001358, A003586, A219528.

Sequence in context: A133764 A163643 A139558 * A110602 A254923 A122635

Adjacent sequences: A219553 A219554 A219555 * A219557 A219558 A219559

Keyword

nonn,easy

Author

Jonathan Vos Post, Nov 22 2012

Status

approved