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Numbers n such that triangular numbers T(n), T(n+1) and T(n+2) are 3-almost primes.
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%I #8 Feb 05 2017 03:36:35

%S 17,28,41,281,2081,2801,4721,5441,6196,12161,12916,13996,20476,24916,

%T 32321,32441,34156,34961,40036,56596,70996,73361,94396

%N Numbers n such that triangular numbers T(n), T(n+1) and T(n+2) are 3-almost primes.

%C Numbers n such that n, n+1 and n+2 are terms in A108815.

%H Charles R Greathouse IV, <a href="/A255200/b255200.txt">Table of n, a(n) for n = 1..10000</a>

%e T(17)=A000217(17)=153=3*3*17, T(18)=A000217(18)=171=3*3*19, T(19)=A000217(19)=171=2*5*19.

%o (PARI) issemi(n)=bigomega(n)==2

%o is(n)=if(n%2, if(n%4==1, isprime((n+3)/4) && isprime(n+2) && isprime(n) && issemi((n+1)/2), isprime((n+1)/4) && isprime(n) && isprime(n+2) && issemi((n+3)/2)), if(n%4==2, isprime((n+2)/4) && isprime(n+1) && isprime(n+3) && issemi(n/2), isprime(n/4) && isprime(n+1) && isprime(n+3) && issemi(n/2+1))) \\ _Charles R Greathouse IV_, Feb 05 2017

%Y Cf. A000217, A075875, A108815.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 16 2015