

A282429


List of distinct terms of A282026.


1



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



