A282429 List of distinct terms of A282026.

1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 26, 28, 29, 31

Offset: 1

Author

Altug Alkan and Andrey Zabolotskiy, Feb 15 2017, following a suggestion from N. J. A. Sloane

Keywords

• nonn
• more

Comments

a(n) occurs in A282026 for the first time at the position A282423(a(n)).

Examples

			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.
		

Crossrefs

Cf. A282026, A282423.

Programs

Mathematica

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 *)