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%I #28 Aug 06 2021 05:52:31
%S 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 33,34,36,37,38,39,40,42,43,44,45,46,47,48,49,51,52,54,55,57,58,59,60,
%U 61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80
%N Numbers of the form i+j+2*i*j and 2+i+j+2*i*j for i,j >= 1.
%C Except 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sieve_of_Sundaram">Sieve of Sundaram</a>.
%e For i,j = 1, 1+1+2*1*1 = 4 and 2+1+1+2*1*1 = 6.
%o (Python)
%o def aupto(limit):
%o aset = set()
%o for i in range(1, limit//3):
%o for j in range(i, limit//3):
%o t = i + j + 2*i*j
%o if t > limit: break
%o aset.update([t, t+2])
%o return sorted(an for an in aset if an <= limit)
%o print(aupto(80)) # _Michael S. Branicky_, Jul 05 2021
%Y Cf. A046132, A023200.
%Y Union of A047845 and A153043, except 0 and 2.
%K nonn
%O 1,1
%A _Davide Rotondo_, Jun 19 2021
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