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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 Eric Weisstein's World of Mathematics, Prime Arithmetic Progression. Wikipedia, Primes in arithmetic progression. 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 June 19 02:57 EDT 2021. Contains 345125 sequences. (Running on oeis4.)