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A219556 Semiprimes neighboring a 3-smooth number. 0
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 (list; graph; refs; listen; history; text; internal format)
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, which may be called "Near-3-smooth semiprimes."

LINKS

Table of n, a(n) for n=1..54.

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

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Last modified February 19 16:23 EST 2018. Contains 299356 sequences. (Running on oeis4.)