A211889 Smallest positive d such that prime(n)+k*d is prime for 0 <= k <= n.

1, 2, 6, 30, 60, 244230, 6930, 546840, 3120613860, 7399357350, 10719893274090, 173761834256010, 14772517344885300

Offset: 1

Author

Reinhard Zumkeller, Jul 13 2012

Keywords

• nonn
• more

Comments

a(n) = A211890(n,k+1) - A211890(n,k), 0 <= k < n.

Links

• Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
• Wikipedia, Primes in arithmetic progression.
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A000040, A010051, A211890.

Programs

Haskell

a211889 n = head [k | let p = a000040 n, k <- [1..],
            all ((== 1) . a010051') $ map ((+ p) . (* k)) (a002260_row n)]

Python

from sympy import isprime, prime, primorial, primepi
def A211889(n):
    if n == 1:
        return 1
    delta = primorial(primepi(n))
    p, d = prime(n), delta
    while True:
        q = p
        for _ in range(n):
            q += d
            if not isprime(q):
                break
        else:
            return d
        d += delta # Chai Wah Wu, Jun 28 2019

Formula

A010051(A000040(n) + k * a(n)) = 1, 0 <= k <= n.

Extensions

a(10) from Chai Wah Wu, Jun 29 2019

a(11)-a(13) from Giovanni Resta, Jun 30 2019