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A263990 Nonsquare numbers k such that k and k + 1 are semiprimes. 7


%S 14,21,33,34,38,57,85,86,93,94,118,122,133,141,142,145,158,177,201,

%T 202,205,213,214,217,218,253,298,301,302,326,334,381,393,394,445,446,

%U 453,481,501,514,526,537,542,553,565,622,633,634,694,697,698,706,717,745,766,778,793,802,817,842,865,878

%N Nonsquare numbers k such that k and k + 1 are semiprimes.

%C If n and n+1 are semiprimes then n+1 is always nonsquare while n can be a full square (see A263951). The sequence gives the nonsquare terms of A070552. Each of the numbers n and n+1 is a product of two distinct primes.

%C Numbers that are terms in A070552 but not in A263951.

%C The subsequence of triples of consecutive squarefree semiprimes is A039833. - _R. J. Mathar_, Aug 13 2019

%H Seiichi Manyama, <a href="/A263990/b263990.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[1000], ! IntegerQ[Sqrt[#]] && 2 == PrimeOmega[#] == PrimeOmega[# + 1] &]

%o (PARI) is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2 && !isprimepower(n), isprime(n/2) && bigomega(n+1)==2) \\ _Charles R Greathouse IV_, Apr 25 2016

%Y Subsequence of A070552, A086263.

%Y Cf. A006881, A263951.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 31 2015

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Last modified November 14 00:05 EST 2019. Contains 329106 sequences. (Running on oeis4.)