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.

Showing 1-3 of 3 results.

A220142 The values of k in A220141.

Original entry on oeis.org

2, 6, 18, 24, 42, 54, 120, 258, 396, 480, 612, 840, 1074, 1800, 2130, 2172, 2256, 2550, 2694, 3282, 3492, 3690, 3810, 4110, 4626, 4788, 4860, 4992, 5148, 5280, 5958, 5994, 6804, 7920, 9654, 9660, 11082, 16134
Offset: 1

Views

Author

T. D. Noe, Jan 08 2013

Keywords

Crossrefs

Cf. A071407, A220141.

Programs

  • Mathematica
    t = {{2, 2}}; Do[k = 1; While[! (PrimeQ[k*n - 1] && PrimeQ[k*n + 1]), k++]; If[k > t[[-1, 2]], AppendTo[t, {n, k}]], {n, Prime[Range[2, 1000]]}]; Transpose[t][[2]]

Extensions

More terms from Amiram Eldar, Dec 30 2019

A071407 Least k such that k*prime(n) + 1 and k*prime(n) - 1 are twin primes.

Original entry on oeis.org

2, 2, 6, 6, 18, 24, 6, 12, 6, 12, 42, 54, 30, 24, 6, 120, 18, 258, 24, 18, 84, 132, 54, 48, 114, 42, 6, 6, 48, 24, 144, 30, 6, 12, 12, 78, 24, 36, 30, 54, 132, 18, 90, 36, 66, 18, 42, 30, 120, 30, 36, 42, 18, 18, 54, 84, 60, 12, 210, 12, 6, 60, 150, 102, 6, 210, 30, 24, 6
Offset: 1

Views

Author

Labos Elemer, May 24 2002

Keywords

Comments

Note that 6 divides a(n) for n > 2. - T. D. Noe, Jan 07 2013

Examples

			n=4: prime(4)=7, a(4)=6 because 6*prime(4)=42 and {41,43} are primes.

Links

Crossrefs

Cf. A071256, A071404-A071406, A060256, A060210, A090530, A294731.
Cf. A071558 (k at every integer).
Cf. A220141, A220142 (record values).

Programs

  • Haskell
    a071407 n = head [k | k <- [2,4..], let x = k * a000040 n,
                      a010051' (x - 1) == 1, a010051' (x + 1) == 1]
-- Reinhard Zumkeller, Feb 14 2013
  • Mathematica
    Table[fl=1; Do[s=(Prime[j])*k; If[PrimeQ[s-1]&&PrimeQ[s+1]&&Equal[fl, 1], Print[{j, k}]; fl=0], {k, 1, 2*j^2}], {j, 0, 100}]

Formula

From Amiram Eldar, Aug 25 2025: (Start)
a(n) = A090530(n) / prime(n).
a(n) = 6 * A294731(n) for n >= 3. (End)

A257771 Numbers n such that n*k - 1 and n*k + 1 are not both prime for any k < n.

Original entry on oeis.org

1, 2, 5, 8, 11, 13, 31, 37, 53, 61, 73, 79, 97, 122, 127
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 07 2015

Keywords

Comments

Numbers n such that A071558(n) > n.

Crossrefs

Cf. A071558, A220141.

Programs

  • PARI
    is(n)=for(k=1,n-1,if(isprime(n*k-1)&&isprime(n*k+1), return(0))); 1 \\ Charles R Greathouse IV, May 08 2015
  • PARI
    is(n)=my(s=6/gcd(n,6)); forstep(k=s,n-1,s, if(isprime(n*k-1)&&isprime(n*k+1), return(0))); 1 \\ Charles R Greathouse IV, May 08 2015
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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