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A345447 Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.

%I A345447 #31 May 25 2024 19:36:08
%S A345447 4,6,7,9,10,12,13,14,15,16,17,18,19,21,22,24,25,26,27,28,29,30,31,32,
%T A345447 33,34,36,37,38,39,40,42,43,44,45,46,47,48,49,51,52,54,55,57,58,59,60,
%U A345447 61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80
%N A345447 Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.
%C A345447 Except for 1 and 2 the complement sequence c is: 3, 5, 8, 11, 20, 23, 35, 41, 50, 53, 56, 65, ...; where 2*c(i) + 1 and 2*c(i) - 3 are a pair of cousin primes. This is a consequence of the sieve of Sundaram.
%H A345447 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sieve_of_Sundaram">Sieve of Sundaram</a>.
%e A345447 For i,j = 1, 1+1+2*1*1 = 4 and 2+1+1+2*1*1 = 6.
%o A345447 (Python)
%o A345447 def aupto(limit):
%o A345447     aset = set()
%o A345447     for i in range(1, limit//3):
%o A345447         for j in range(i, limit//3):
%o A345447             t = i + j + 2*i*j
%o A345447             if t > limit: break
%o A345447             aset.update([t, t+2])
%o A345447     return sorted(an for an in aset if an <= limit)
%o A345447 print(aupto(80)) # _Michael S. Branicky_, Jul 05 2021
%Y A345447 Cf. A046132, A023200.
%Y A345447 Union of A047845 and A153043, except for 0 and 2.
%K A345447 nonn
%O A345447 1,1
%A A345447 _Davide Rotondo_, Jun 19 2021