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A256386 Numbers m such that m-2, m-1, m+1, m+2 cannot all be represented in the form x*y + x + y for values x, y with x >= y > 1.

%I A256386 #31 Apr 21 2022 14:04:57
%S A256386 2,3,4,5,8,11,59,1319,1619,4259,5099,6659,6779,11699,12539,21059,
%T A256386 66359,83219,88259,107099,110879,114659,127679,130199,140759,141959,
%U A256386 144539,148199,149519,157559,161339,163859,175079,186479,204599,230939,249539,267959,273899,312839
%N A256386 Numbers m such that m-2, m-1, m+1, m+2 cannot all be represented in the form x*y + x + y for values x, y with x >= y > 1.
%C A256386 Indices of terms surrounded by pairs of zeros in A255361.
%C A256386 Conjectures:
%C A256386 1. A255361(a(n)) > 0 for n > 4.
%C A256386 2. All terms > 8 are primes.
%C A256386 3. All terms > 8 are terms of these supersequences: A118072, A171667, A176821, A181602, A181669.
%C A256386 From _Lamine Ngom_, Feb 12 2022: (Start)
%C A256386 For n > 4, a(n) is not a term of A254636. This means that a(n)-2, a(n)-1, a(n)+1 and a(n)+2 are adjacent terms in A254636.
%C A256386 Number of terms < 10^k: 5, 7, 7, 13, 19, 96, 441, 2552, ...
%C A256386 Conjecture 2 would follow if we establish the equivalence "t is in sequence" <=> "t is a term of b(n): lesser of twin primes pair p and q such that (p - 1)/2 and (q + 1)/2 are also a pair of twin primes (A077800)".
%C A256386 It appears that b(n) = a(n) for n > 5. Verified for all terms < 10^9. (End)
%F A256386 a(n) = A158870(n-5) - 2, n > 5 (conjectured). - _Lamine Ngom_, Feb 12 2022
%e A256386 9, 10, 12, 13 cannot be represented as x*y + x + y, where x >= y > 1. Therefore 11 is in the sequence.
%Y A256386 Cf. A255361, A254636.
%Y A256386 Cf. A118072, A171667, A176821, A181602, A181669.
%Y A256386 Cf. A001097, A001359, A006512, A077800, A158870.
%K A256386 nonn
%O A256386 1,1
%A A256386 _Alex Ratushnyak_, Mar 31 2015