cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A263990 #29 Aug 08 2025 03:24:43
%S A263990 14,21,33,34,38,57,85,86,93,94,118,122,133,141,142,145,158,177,201,
%T A263990 202,205,213,214,217,218,253,298,301,302,326,334,381,393,394,445,446,
%U A263990 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 A263990 Nonsquare numbers k such that k and k+1 are semiprimes.
%C A263990 If k and k+1 are semiprimes then k+1 is always nonsquare while k can be a square (see A263951). The sequence gives the nonsquare terms of A070552. Each of the numbers k and k+1 is a product of two distinct primes.
%C A263990 Numbers that are terms in A070552 but not in A263951.
%C A263990 The subsequence of triples of consecutive squarefree semiprimes is A039833. - _R. J. Mathar_, Aug 13 2019
%H A263990 Seiichi Manyama, <a href="/A263990/b263990.txt">Table of n, a(n) for n = 1..10000</a>
%F A263990 a(n) = A109288(n) - 1. - _Amiram Eldar_, Aug 08 2025
%t A263990 Select[Range[1000], ! IntegerQ[Sqrt[#]] && 2 == PrimeOmega[#] == PrimeOmega[# + 1] &]
%o A263990 (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 A263990 Subsequence of A070552, A086263.
%Y A263990 Cf. A006881, A039833, A109288, A263951.
%K A263990 nonn
%O A263990 1,1
%A A263990 _Zak Seidov_, Oct 31 2015