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Semiprimes in A056105.
10

%I #16 Oct 09 2022 05:21:35

%S 9,22,134,177,226,482,737,1046,1282,1681,1977,2641,3202,3401,3817,

%T 4034,4486,5462,5721,6817,7401,7702,8966,9634,9977,10681,11042,11409,

%U 12937,15409,16726,17177,18566,21506,28617,29801

%N Semiprimes in A056105.

%C Intersection of A056105 and A001358.

%H Michael De Vlieger, <a href="/A113519/b113519.txt">Table of n, a(n) for n = 1..10000</a>

%e A056105(44) = 3*44^2 - 2*44 + 1 = 5721 = 3 * 1907 which is a semiprime.

%e A056105(24) = 3*24^2 - 2*24 + 1 = 1681 = 41^2 which is a semiprime (the two prime factors need not be distinct).

%e A056105(100) = 3*100^2 - 2*100 + 1 = 29801 = 17 * 1753, which is a semiprime.

%p for n from 0 to 300 do

%p s := 3*n^2-2*n+1 ;

%p if isA001358(s) then

%p printf("%d,",s) ;

%p end if;

%p end do: # _R. J. Mathar_, Jun 30 2020

%t Select[Array[3 #^2 - 2 # + 1 &, 100], PrimeOmega[#] == 2 &] (* _Michael De Vlieger_, Mar 17 2021 *)

%Y Cf. A001358, A056105.

%Y Cf. A113524, A113525, A113527, A113528, A113530.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 12 2006