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%I #12 Feb 18 2017 22:05:02
%S 1,2,4,5,7,8,11,13,14,16,17,19,22,23,26,28,29,31
%N List of distinct terms of A282026.
%C a(n) occurs in A282026 for the first time at the position A282423(a(n)).
%e 3 is not a term. Proof: Suppose 3 is a term of A282026. For the corresponding n, 2*n + 1 cannot be divisible by 3 because of A282026’s definition (gcd(3, 2*n + 1) = 1). So 2*n + 1 can be only of the form 6*k + 1 or 6*k + 5. But 6*k + 1 + 2*1 and 6*k + 5 + 2*2 are both composite numbers and 1, 2 are relatively prime to any odd number. Since they are smaller than 3, this is the contradiction to the assumption that 3 is the term which is the smallest number for corresponding n. This also proves that 3*k cannot be a term of this sequence for any k >= 1.
%t Union@ Table[m = 1; While[Nand[CoprimeQ[m, 2 n + 1], CompositeQ[2 (n + m) + 1]], m++]; m, {n, 0, 10^7}] (* _Michael De Vlieger_, Feb 18 2017 *)
%Y Cf. A282026, A282423.
%K nonn,more
%O 1,2
%A _Altug Alkan_ and _Andrey Zabolotskiy_, Feb 15 2017, following a suggestion from _N. J. A. Sloane_
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