A282423 a(n) = smallest k such that A282026(k) = n, or 0 if no such k exists.

3, 2, 0, 13, 19, 0, 427, 4, 0, 0, 1, 0, 802, 99412, 0, 3097, 7, 0, 637, 0, 0, 7225627, 30898822, 0, 0, 280134277, 0, 31705902442, 43190647, 0, 965577112

Offset

1,1

Comments

a(n) is nonzero if n is in A282429.

For n>4 and nonzero a(n), 2*a(n)+3 is in A022004. For n>8 and nonzero a(n), 2*a(n)+3 is also in A153417. For n>16 and nonzero a(n), 2*a(n)+3 is also in A049481.

Links

Table of n, a(n) for n=1..31.

Example

a(10) = 0. Proof: Suppose 10 is a term of A282026. For the corresponding n, 2*n + 1 cannot be divisible by 5 because of A282026’s definition (gcd(10, 2*n + 1) = 1). So 2*n + 1 can be only of the form 10*k + 1, 10*k + 3, 10*k + 7, 10*k + 9. But 10*k + 1 + 2*2, 10*k + 3 + 2*1, 10*k + 7 + 2*4, 10*k + 9 + 2*8 are all composite and 1, 2, 4, 8 are relatively prime to any odd number. Since all of them are smaller than 10, this is the contradiction to the assumption that 10 is the term which is the smallest number for corresponding n. This also proves that a(5*k) = 0 for any k > 1.

Crossrefs

Cf. A282026, A282429.

Sequence in context: A067346 A360282 A356654 * A111541 A371025 A244134

Adjacent sequences: A282420 A282421 A282422 * A282424 A282425 A282426

Keyword

nonn,more

Author

Andrey Zabolotskiy and Altug Alkan, Feb 14 2017, following a suggestion from N. J. A. Sloane

Status

approved