A071558 Smallest k such that n*k + 1 and n*k - 1 are twin primes.

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

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

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 A350788 A282698

Adjacent sequences: A071555 A071556 A071557 * A071559 A071560 A071561

Keyword

easy,nonn

Author

Benoit Cloitre, May 30 2002

Status

approved