A174649 Numbers k such that semiprime(k)+/-1 are both semiprime.

12, 29, 33, 41, 47, 64, 70, 73, 96, 124, 137, 194, 211, 254, 277, 308, 333, 372, 395, 416, 471, 507, 529, 544, 560, 573, 602, 624, 637, 657, 672, 687, 696, 716, 752, 764, 767, 869, 949, 1003, 1025, 1069, 1079, 1090, 1176, 1212, 1242, 1261, 1343, 1523, 1553

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(1) = 12 because 12th semiprime = 2*17, 2*17-1 = 3*11 and 2*17+1 = 5*7;
a(2) = 29 because 29th semiprime = 2*43, 2*43-1 = 5*17 and 2*43+1 = 3*29.

Mathematica

Flatten[Position[Select[Range[7000], PrimeOmega[#]==2&], _?(PrimeOmega[#-1] == PrimeOmega[#+1]==2&)]] (* Harvey P. Dale, Dec 18 2012 *)

Prog

(Python)
from sympy import factorint
from itertools import count, islice
def semiprimes():
    for i in count(1):
        if sum(factorint(i).values()) == 2:
            yield i
def agen():
    g = semiprimes()
    prevsp, sp, nextsp = next(g), next(g), next(g)
    for k in count(2):
        if nextsp - prevsp == 2:
            yield k
        prevsp, sp, nextsp = sp, nextsp, next(g)
print(list(islice(agen(), 51))) # Michael S. Branicky, Dec 29 2021

Crossrefs

Cf. A001358.

Sequence in context: A000546 A130516 A045554 * A161452 A353872 A212867

Adjacent sequences: A174646 A174647 A174648 * A174650 A174651 A174652

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 25 2010

Extensions

Corrected by Ray Chandler, Apr 06 2010

Status

approved