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A211889 Smallest positive d such that prime(n)+k*d is prime for 0 <= k <= n. 3
1, 2, 6, 30, 60, 244230, 6930, 546840, 3120613860, 7399357350, 10719893274090, 173761834256010, 14772517344885300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.

Wikipedia, Primes in arithmetic progression.

Index entries for sequences related to primes in arithmetic progressions

FORMULA

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

PROG

(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

CROSSREFS

Cf. A000040, A010051, A211890.

Sequence in context: A127517 A137825 A008341 * A174276 A117849 A328417

Adjacent sequences:  A211886 A211887 A211888 * A211890 A211891 A211892

KEYWORD

nonn,more

AUTHOR

Reinhard Zumkeller, Jul 13 2012

EXTENSIONS

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

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

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)