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 13 results. Next

A191001 Indices k where A191620(k) = A191751(k).

Original entry on oeis.org

1, 2, 4, 5, 9, 10, 18, 26, 34, 38, 45, 50, 57, 88, 108, 115, 161, 208, 224, 225, 238, 240, 264, 354, 597, 634, 984, 1008, 1080, 1468
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 15 2011

Keywords

Examples

			1 is a term because A191620(1) = A191751(1) = 0;
2 is a term because A191620(2) = A191751(2) = 1.

Crossrefs

Cf. A191620, A191751.

Programs

  • Maple
    A191751 := proc(n) local k; for k from 0 do if isprime((2^n-1)*2^n-k) then return k: end if : end do: end proc:
A191620 := proc(n) local k: for k from 0 do if isprime((2^n-k)*2^n-1) then return k: end if: end do: end proc:
for n from 1 do if A191751(n) = A191620(n) then printf("%d,\n",n); end if; end do: # R. J. Mathar, Jun 25 2011

Formula

{k: A191620(k)=A191751(k)}.

Extensions

a(25)-a(30) from Jinyuan Wang, May 15 2020

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 *)

A191618 Least a such that (2^n+a)*2^n - 1 is prime.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 11, 2, 2, 1, 13, 2, 4, 22, 2, 1, 2, 2, 43, 4, 2, 13, 2, 1, 13, 1, 2, 46, 8, 29, 83, 2, 8, 34, 1, 11, 19, 31, 25, 7, 38, 31, 31, 76, 52, 31, 43, 32, 13, 92, 2, 1, 59, 22, 1, 16, 19, 11, 16, 74, 8, 13, 8, 74, 2, 121, 20, 49, 85, 134, 116, 16
Offset: 1

Views

Author

Pierre CAMI, Jun 09 2011

Keywords

Links

Crossrefs

Cf. A191617, 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 *)

A205322 Smallest k>=0 such that (2^n-k)*2^n-1 and (2^n-k)*2^n+1 are a twin prime pair; or -1 if no such k exists.

Original entry on oeis.org

0, 1, -1, 1, 26, 22, 8, 28, 47, 16, 14, 19, 17, 316, 8, 133, 116, 166, 77, 364, 197, 49, 647, 1594, 848, 109, 869, 169, 773, 166, 1274, 466, 512, 694, 644, 733, 401, 1636, 662, 184, 71, 3106, 1157, 346, 332, 2194, 6179, 7999, 6023, 6784, 5612, 1108, 1001, 649, 197
Offset: 1

Views

Author

Pierre CAMI, Jul 14 2012

Keywords

Comments

Conjecture: there is always at least one k>=0 unless n=3.

Links

Crossrefs

Cf. A191619, A191620, A205321.

Programs

  • Maple
    A205322 := proc(n)
    local a,p ;
    for a from 0 to 2^n do
         p := (2^n-a)*2^n-1 ;
        if isprime(p) and isprime(p+2) then
            return a;
        end if;
    end do:
    return -1 ;
end proc: # R. J. Mathar, Jul 18 2012
  • Mathematica
    Table[k = -1; While[k++; p = 4^n - k*2^n - 1; p > 0 && ! (PrimeQ[p] && PrimeQ[p + 2])]; If[p <= 0, -1, k], {n, 50}] (* T. D. Noe, Mar 15 2013 *)

A191751 Least k such that (2^n-1)*2^n - k is a prime number.

Original entry on oeis.org

0, 1, 3, 1, 1, 5, 3, 11, 1, 1, 25, 29, 3, 13, 3, 7, 39, 1, 13, 23, 3, 5, 69, 11, 39, 13, 15, 31, 99, 83, 117, 31, 9, 11, 25, 67, 45, 1, 39, 47, 45, 71, 69, 77, 1, 131, 67, 101, 55, 1, 9, 41, 13, 43, 33, 233, 1, 113, 7, 29, 45, 55, 99, 41, 261, 5, 15, 343, 9
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jun 14 2011, Jun 15 2011

Keywords

Examples

			a(1)=0 because (2^1-1)*2^1 - 0 =    2 is prime,
a(2)=1 because (2^2-1)*2^2 - 1 =   11 is prime,
a(3)=3 because (2^3-1)*2^3 - 3 =   53 is prime,
a(4)=1 because (2^4-1)*2^4 - 1 =  239 is prime,
a(5)=1 because (2^5-1)*2^5 - 1 =  991 is prime,
a(6)-5 because (2^6-1)*2^6 - 5 = 4027 is prime.

Links

Crossrefs

Cf. A098845, A191001, A191620.
Cf. A020522 ((2^n-1)*2^n).

Programs

  • Maple
    a := proc(n) local k: for k from 0 do if(isprime((2^n-1)*2^n-k))then return k: fi: od: end: seq(a(n), n=1..69); # Nathaniel Johnston, Jun 14 2011
  • Mathematica
    lk[n_]:=Module[{c=2^n,k=0},While[!PrimeQ[c(c-1)-k],k++];k]; Array[lk,70] (* Harvey P. Dale, Jul 02 2018 *)
  • PARI
    a(n) = my(x=(2^n-1)*2^n); x - precprime(x); \\ Michel Marcus, Feb 21 2019
Showing 1-10 of 13 results. Next

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