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.

A290435 Semiprimes of the form pq where p < q and p+q+1 is prime.

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%I A290435 #15 Aug 02 2017 15:37:25
%S A290435 21,35,39,55,57,65,77,85,111,115,129,155,161,185,187,201,203,205,209,
%T A290435 221,235,237,265,291,299,305,309,319,323,327,335,341,365,371,377,381,
%U A290435 391,413,415,437,451,485,489,493,497,505,515,517,535,579,611,623,649,655
%N A290435 Semiprimes of the form pq where p < q and p+q+1 is prime.
%C A290435 Squarefree terms of A290434.
%C A290435 All terms are odd.
%C A290435 A286842(a(n)) = 1 for all n.
%H A290435 Chai Wah Wu, <a href="/A290435/b290435.txt">Table of n, a(n) for n = 1..10000</a>
%e A290435 655 = 5*131 and 5+131+1 is prime, so 655 is a term.
%t A290435 With[{nn = 54}, Take[#, nn] &@ Union@ Flatten@ Table[Function[p, Map[Times @@ # &@ # &, #] &@ Select[Map[{p, #} &, Prime@ Range[PrimePi@ p - 1]], PrimeQ[Total@ # + 1] &]]@ Prime@ n, {n, nn + 4}]] (* _Michael De Vlieger_, Aug 01 2017 *)
%t A290435 With[{nn=60},Take[Times@@@Select[Subsets[Prime[Range[nn]],{2}],PrimeQ[ Total[ #]+ 1]&]//Union,nn]] (* _Harvey P. Dale_, Aug 02 2017 *)
%o A290435 (Python)
%o A290435 from sympy import factorint, isprime
%o A290435 A290435_list = [n for n in range(2,10**5) if sum(factorint(n).values()) == len(factorint(n)) == 2 and isprime(1+sum(factorint(n).keys()))]
%o A290435 (PARI) isok(n) = (bigomega(n)==2) && (omega(n)==2) && isprime(1+vecsum(factor(n)[,1])); \\ _Michel Marcus_, Aug 02 2017
%Y A290435 Cf. A001358, A005117, A006881, A286842, A290434.
%K A290435 nonn
%O A290435 1,1
%A A290435 _Chai Wah Wu_, Aug 01 2017