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

1,2

Comments

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

Links

Table of n, a(n) for n=1..18.

Example

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.

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 *)

Crossrefs

Cf. A282026, A282423.

Sequence in context: A229303 A262978 A112886 * A111040 A191324 A147807

Adjacent sequences: A282426 A282427 A282428 * A282430 A282431 A282432

Keyword

nonn,more

Author

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

Status

approved