A326228 Primes p such that m - p#/6 or p#/6 - n is not in A002822 (twin ranks), where m (resp. n) is the next larger (resp. smaller) twin rank w.r.t. p#/6, and # = A034386 (primorial).

41, 227, 307, 311, 349, 457, 613

Offset

1,1

Comments

Related to the "Twin Fortune Conjecture" (A. Dinculescu) which states that the distance between p#/6 and the next larger or smaller n in A002822 (twin rank, such that 6n +- 1 are twin primes) is again a twin rank; very similar to Fortune's Conjecture, cf. A005235.

For a(1) = 41, the non twin rank is p#/6 - n, for all other terms listed here, it is m - p#/6. However, in these cases, the other distance is a twin rank. For all other primes, both distances are twin ranks.

Links

Table of n, a(n) for n=1..7.

Prog

(PARI) is(p)={ my(m=A034386(p)/6, n=m); until(is_A002822(n-=1), ); (is_A002822(m-n) || ((n=m) && !until(is_A002822(m+=1), ) && is_A002822(m-n))) && isprime(p)}

Crossrefs

Cf. A002822 (twin ranks), A034386 (primorial), A005235 (Fortunate numbers).

Sequence in context: A172085 A251094 A300464 * A142392 A142943 A142183

Adjacent sequences: A326225 A326226 A326227 * A326229 A326230 A326231

Keyword

nonn,hard,more

Author

M. F. Hasler, Jun 24 2019

Status

approved