A329485 Odd numbers k such that there are no consecutive prime numbers p, q such that 2*(p - k) = q + k.

7, 15, 17, 29, 37, 39, 47, 51, 55, 61, 67, 69, 71, 81, 83, 85, 87, 95, 97, 99, 105, 107, 111, 113, 119, 121, 123, 129, 135, 141, 149, 155, 159, 163, 167, 169, 171, 175, 177, 181, 183, 185, 187, 191, 193, 195, 197, 201, 209, 211, 215, 217, 221, 229, 235, 239, 241, 243, 247, 249

Offset

1,1

Comments

The complementary sequence that include the numbers k which do satisfy 2*(p - k) = q + k is {1, 3, 5, 9, 11, 13, 19, 21, 23, 25, 27, 31, 33, 35, 41, 43, 45, 49, 53, 57, 59, ...}. The number 7 does not satisfy the formula, so is the first term of sequence.

The terms of the sequence are the multiples of 3 not included in A062234 and divided by 3.

Links

Table of n, a(n) for n=1..60.

Example

7 is a term because 2*(p - 7) <> q + 7 for every p, q consecutive prime numbers. See comments.

Prog

(PARI) v=vector(1000); forstep(k=1, 299, 2, forprime(n=2, 1000, p=nextprime(n+1); if(2*(n-k)==p+k, v[k]=1; break))); forstep(k=1, 250, 2, if(v[k]==0, print1(k", ")))

Crossrefs

Cf. A000040, A062234.

Sequence in context: A237054 A216848 A065566 * A154618 A275190 A224891

Adjacent sequences: A329482 A329483 A329484 * A329486 A329487 A329488

Keyword

nonn

Author

Dimitris Valianatos, Nov 14 2019

Status

approved