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 A071558 Smallest k such that n*k + 1 and n*k - 1 are twin primes. 16
 4, 2, 2, 1, 6, 1, 6, 9, 2, 3, 18, 1, 24, 3, 2, 12, 6, 1, 12, 3, 2, 9, 6, 3, 6, 12, 4, 15, 12, 1, 42, 6, 6, 3, 12, 2, 54, 6, 8, 6, 30, 1, 24, 15, 4, 3, 6, 4, 18, 3, 2, 6, 120, 2, 12, 48, 4, 6, 18, 1, 258, 21, 14, 3, 30, 3, 24, 15, 2, 6, 18, 1, 84, 27, 2, 3, 6, 4, 132, 3, 10, 15, 54, 5, 12, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(n) < sqrt(n)*log(n) for all n > 17261. This has been verified for n up to 3*10^7. It implies the inequality a(n) < n for each n > 127. - Zhi-Wei Sun, Jan 07 2013 A200996(n) <= a(n). - Reinhard Zumkeller, Feb 14 2013 LINKS T. D. Noe and Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) MATHEMATICA Table[k=1; While[!And@@PrimeQ[n*k+{1, -1}], k++]; k, {n, 86}] (* Jayanta Basu, May 26 2013 *) PROG (PARI) for(n=1, 100, s=1; while(isprime(s*n+1)*isprime(n*s-1)==0, s++); print1(s, ", ")) (Haskell) a071558 n = head [k | k <- [1..], let x = k * n,                       a010051' (x - 1) == 1, a010051' (x + 1) == 1] -- Reinhard Zumkeller, Feb 14 2013 CROSSREFS Cf. A071256, A001097, A086686, A034693. Cf. A071407 (k at prime n). Cf. A220143, A220144 (record values). Sequence in context: A325527 A088570 A102888 * A179621 A282698 A136709 Adjacent sequences:  A071555 A071556 A071557 * A071559 A071560 A071561 KEYWORD easy,nonn AUTHOR Benoit Cloitre, May 30 2002 STATUS approved

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Last modified October 16 01:28 EDT 2019. Contains 328038 sequences. (Running on oeis4.)