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 1-10 of 10 results.

A191620 Least k such that (2^n-k)*2^n - 1 is a prime number.

Original entry on oeis.org

0, 1, 2, 1, 1, 2, 2, 7, 1, 1, 14, 2, 11, 11, 2, 22, 7, 1, 2, 8, 2, 11, 14, 32, 2, 13, 2, 11, 52, 8, 10, 49, 13, 11, 4, 11, 31, 1, 23, 64, 11, 47, 20, 38, 1, 14, 4, 88, 7, 1, 47, 14, 22, 8, 2, 14, 1, 31, 20, 71, 20, 4, 44, 101, 38, 43, 80, 49, 11, 59, 4, 8
Offset: 1

Views

Author

Pierre CAMI, Jun 09 2011

Keywords

Comments

Does a(n) exist for every n? This does not seem to be known, even on the GRH; see Heath-Brown. [Charles R Greathouse IV, Dec 27 2011]

Links

Crossrefs

Cf. A191617, A191618, A191619, A191621.

Programs

  • Mathematica
    Table[a = 0; While[! PrimeQ[(2^n - a)*2^n - 1], a++]; a, {n, 100}] (* T. D. Noe, Jun 11 2011 *)
  • PARI
    a(n)=forstep(k=4^n-1,1,-2^n,if(ispseudoprime(k),return(2^n-(k+1)>>n))) \\ Charles R Greathouse IV, Dec 27 2011

A191617 Least number a such that (2^n+a)*2^n + 1 is a prime number.

Original entry on oeis.org

0, 0, 1, 0, 4, 3, 12, 0, 1, 3, 6, 6, 16, 9, 4, 5, 3, 20, 6, 5, 4, 5, 21, 9, 16, 35, 6, 6, 18, 8, 28, 6, 46, 11, 39, 6, 3, 20, 22, 47, 93, 90, 13, 51, 27, 98, 34, 6, 12, 14, 21, 21, 49, 143, 18, 5, 58, 30, 37, 30, 6, 56, 16, 150, 72, 59, 12, 5, 34, 3, 28, 45
Offset: 1

Views

Author

Pierre CAMI, Jun 09 2011

Keywords

Links

Crossrefs

Cf. A191618, A191619, A191620, A191621.

Programs

  • Mathematica
    Table[a = 0; While[! PrimeQ[(2^n + a)*2^n + 1], a++]; a, {n, 100}] (* T. D. Noe, Jun 11 2011 *)

A191619 Least a such that (2^n-a)*2^n + 1 is a prime number.

Original entry on oeis.org

0, 0, 3, 0, 3, 10, 3, 0, 3, 10, 3, 4, 3, 4, 3, 16, 23, 4, 3, 21, 12, 10, 18, 40, 14, 37, 8, 16, 32, 10, 36, 1, 63, 10, 3, 48, 17, 67, 3, 31, 33, 22, 9, 19, 3, 9, 47, 33, 21, 15, 3, 58, 51, 22, 78, 163, 8, 30, 3, 85, 44, 4, 71, 28, 204, 4, 42, 75, 27, 16, 17
Offset: 1

Views

Author

Pierre CAMI, Jun 09 2011

Keywords

Comments

Does a(n) exist for every n? This does not seem to be known, even on the GRH; see Heath-Brown. [Charles R Greathouse IV, Dec 27 2011]

Links

Crossrefs

Cf. A191617, A191618, A191620, A191621.

Programs

  • Mathematica
    Table[a = 0; While[! PrimeQ[(2^n - a)*2^n + 1], a++]; a, {n, 100}] (* T. D. Noe, Jun 11 2011 *)
  • PARI
    a(n)=forstep(k=4^n+1, 1, -2^n, if(ispseudoprime(k), return(2^n-(k-1)>>n))) \\ Charles R Greathouse IV, Dec 27 2011

A200920 Least k such that (3^n+ k)*3^n + 1 is a prime number.

Original entry on oeis.org

1, 3, 1, 5, 3, 25, 11, 5, 13, 13, 9, 7, 3, 9, 17, 7, 29, 25, 71, 49, 7, 9, 7, 9, 11, 39, 7, 25, 107, 3, 67, 59, 49, 89, 67, 29, 113, 5, 33, 7, 19, 53, 3, 5, 47, 121, 39, 7, 407, 25, 7, 215, 29, 23, 89, 5, 33, 25, 113, 45, 49, 109, 53, 17, 109, 311, 91, 145, 43
Offset: 1

Views

Author

Michel Lagneau, Nov 24 2011

Keywords

Crossrefs

Cf. A191617, A191618, A191619, A191620, A200921, A200922, A200923.

Programs

  • Mathematica
    Table[k = 0; While[!PrimeQ[(3^n + k)*3^n + 1], k++]; k, {n, 72}]

A200921 Least k such that (3^n + k)*3^n - 1 is a prime number.

Original entry on oeis.org

1, 1, 3, 3, 13, 9, 15, 3, 1, 13, 29, 1, 5, 53, 25, 9, 23, 1, 69, 13, 3, 3, 17, 1, 5, 117, 5, 13, 45, 51, 3, 11, 31, 73, 49, 43, 11, 83, 93, 277, 171, 383, 39, 11, 3, 31, 55, 61, 61, 13, 73, 107, 65, 137, 53, 39, 467, 53, 233, 277, 17, 53, 109, 177, 151, 97, 13
Offset: 1

Views

Author

Michel Lagneau, Nov 24 2011

Keywords

Crossrefs

Cf. A191617, A191618, A191619, A191620, A200920, A200922, A200923.

Programs

  • Mathematica
    Table[k = 0; While[!PrimeQ[(3^n + k)*3^n - 1], k++]; k, {n, 72}]
lk[n_]:=Module[{c=3^n,k=0},While[!PrimeQ[(c+k)c-1],k++];k]; Array[lk,70] (* Harvey P. Dale, Aug 19 2015 *)

A200922 Least k such that (3^n - k)*3^n - 1 is a prime number.

Original entry on oeis.org

1, 1, 1, 3, 7, 1, 1, 13, 17, 17, 7, 43, 25, 3, 41, 29, 57, 11, 21, 1, 25, 29, 17, 27, 15, 7, 11, 63, 15, 237, 73, 21, 43, 229, 1, 1, 73, 3, 253, 63, 7, 179, 3, 289, 97, 157, 7, 59, 95, 237, 33, 47, 3, 31, 43, 141, 157, 63, 137, 101, 387, 109, 157, 27, 29, 37
Offset: 1

Views

Author

Michel Lagneau, Nov 24 2011

Keywords

Crossrefs

Cf. A191617, A191618, A191619, A191620,A200920, A200921, A200923.

Programs

  • Mathematica
    Table[k = 0; While[!PrimeQ[(3^n - k)*3^n - 1], k++]; k, {n, 72}]

A200923 Least k such that (3^n - k)*3^n + 1 is a prime number.

Original entry on oeis.org

1, 1, 7, 1, 3, 1, 7, 5, 9, 29, 19, 1, 7, 49, 49, 9, 23, 1, 3, 29, 53, 39, 41, 35, 7, 5, 51, 33, 3, 81, 83, 15, 21, 31, 61, 69, 67, 87, 27, 5, 19, 55, 153, 35, 99, 31, 23, 49, 47, 95, 3, 115, 89, 55, 23, 61, 139, 49, 87, 5, 153, 87, 269, 113, 67, 207, 41, 33
Offset: 1

Views

Author

Michel Lagneau, Nov 24 2011

Keywords

Crossrefs

Cf. A191617, A191618, A191619, A191620, A200920, A200921, A200922.

Programs

  • Mathematica
    Table[k = 0; While[!PrimeQ[(3^n - k)*3^n + 1], k++]; k, {n, 72}]
lk[n_]:=Module[{c=3^n,k=1},While[!PrimeQ[(c-k)*c+1],k++];k]; Array[lk,70] (* Harvey P. Dale, Jul 15 2017 *)

A205321 Smallest k>=0 such that (2^n+k)*2^n-1 and (2^n+k)*2^n+1 are a twin prime pair.

Original entry on oeis.org

0, 11, 1, 11, 4, 11, 13, 116, 34, 14, 241, 44, 97, 458, 337, 59, 604, 206, 67, 167, 424, 179, 97, 326, 259, 284, 1177, 77, 328, 356, 508, 74, 1798, 749, 2197, 1289, 643, 839, 1171, 1427, 814, 2564, 31, 4244, 379, 5099, 3706, 4871, 2719, 3194, 7057, 122, 5329, 2636, 301, 2852, 3793
Offset: 1

Views

Author

Pierre CAMI, Jul 14 2012

Keywords

Comments

Conjecture : there is at least one k for each n.

Links

Crossrefs

Cf. A191617, A191618, A205322

Programs

  • Maple
    A205321 := proc(n)
    local a,p ;
    for a from 0 do
         p := (2^n+a)*2^n-1 ;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 18 2012

Formula

a(n) = A082466(2^n), n>1. - R. J. Mathar, Jul 20 2012

A201134 Least k such that (5^n + k)*5^n - 1 is a prime number.

Original entry on oeis.org

1, 17, 1, 1, 5, 5, 55, 25, 37, 1, 53, 5, 53, 35, 47, 31, 127, 11, 1, 17, 11, 59, 71, 5, 155, 23, 11, 1, 13, 47, 43, 71, 17, 77, 53, 41, 13, 277, 47, 5, 143, 185, 157, 371, 43, 127, 119, 61, 221, 79, 131, 19, 49, 241, 7, 121, 11, 551, 157, 335, 13, 17, 13
Offset: 1

Views

Author

Michel Lagneau, Nov 27 2011

Keywords

Crossrefs

Cf. A191618, A200921.

Programs

  • Mathematica
    Table[k = 0; While[!PrimeQ[(5^n + k)*5^n - 1], k++]; k, {n, 85}]

A201457 Least k such that (7^n + k)*7^n - 1 is a prime number.

Original entry on oeis.org

5, 11, 1, 11, 23, 29, 17, 31, 13, 37, 61, 11, 35, 149, 17, 151, 17, 17, 17, 13, 59, 17, 73, 47, 43, 13, 113, 77, 119, 97, 125, 83, 13, 421, 103, 103, 77, 23, 23, 79, 5, 107, 7, 37, 59, 113, 11, 1, 169, 887, 137, 41, 113, 71, 277, 413, 97, 91, 227, 337, 97, 353, 233, 953, 5, 139, 77, 473, 73, 167, 275, 67, 49, 97, 365, 73, 223, 241, 115
Offset: 1

Views

Author

Michel Lagneau, Dec 01 2011

Keywords

Crossrefs

Cf. A191618, A200921, A201134.

Programs

  • Mathematica
     Table[k = 0; While[!PrimeQ[(7^n + k)*7^n - 1], k++]; k, {n, 85}]
Showing 1-10 of 10 results.

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