cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Benoit Cloitre, May 30 2002

Keywords

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

Crossrefs

Cf. A071256, A001097, A086686, A034693.
Cf. A071407 (k at prime n).
Cf. A220143, A220144 (record values).

Programs

  • Haskell
    a071558 n = head [k | k <- [1..], let x = k * n,
                      a010051' (x - 1) == 1, a010051' (x + 1) == 1]
-- Reinhard Zumkeller, Feb 14 2013
  • Mathematica
    Table[k=1; While[!And@@PrimeQ[n*k+{1,-1}],k++]; k,{n,86}] (* Jayanta Basu, May 26 2013 *)
  • PARI
    a(n) = my(s=1); while(isprime(s*n+1)*isprime(n*s-1)==0, s++); s;

A220143 Numbers n that yield a new record for k such that n*k+1 and n*k-1 are twin primes.

Original entry on oeis.org

1, 5, 8, 11, 13, 31, 37, 53, 61, 433, 1957, 2047, 2603, 4079, 9967, 10789, 76943, 81439, 121763, 206867, 233969, 276349, 495931, 626939, 2055943, 3144937, 3585509, 3810949, 6274823, 8407129, 9299471, 19279903, 35531621, 36426301, 38235389, 71701529, 76384717, 98566373
Offset: 1

Views

Author

T. D. Noe, Jan 08 2013

Keywords

Comments

These are numbers at which A071558 reaches a new record. The corresponding values of k are in A220144. Note that these numbers are not all primes.

Crossrefs

Cf. A071558, A220144.

Programs

  • Mathematica
    t = {{1, 4}}; Do[k = 1; While[! (PrimeQ[k*n - 1] && PrimeQ[k*n + 1]), k++]; If[k > t[[-1, 2]], AppendTo[t, {n, k}]], {n, 2, 100000}]; Transpose[t][[1]]

Extensions

More terms from Amiram Eldar, Dec 30 2019
Showing 1-2 of 2 results.

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