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 1-7 of 7 results.

A127591 Numbers k such that 64k+21 is prime.

Original entry on oeis.org

2, 4, 10, 13, 17, 19, 20, 22, 23, 25, 29, 32, 37, 44, 50, 53, 55, 58, 59, 62, 68, 79, 83, 88, 89, 94, 95, 97, 100, 107, 109, 113, 118, 122, 134, 142, 143, 152, 155, 157, 158, 163, 167, 169, 173, 193, 194, 199, 200
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[21 + 64 n], AppendTo[a, n]], {n, 0, 200}]; a
    Select[Range[200],PrimeQ[64#+21]&] (* Harvey P. Dale, Jan 15 2016 *)

A127592 Primes of the form 64k+21.

Original entry on oeis.org

149, 277, 661, 853, 1109, 1237, 1301, 1429, 1493, 1621, 1877, 2069, 2389, 2837, 3221, 3413, 3541, 3733, 3797, 3989, 4373, 5077, 5333, 5653, 5717, 6037, 6101, 6229, 6421, 6869, 6997, 7253, 7573, 7829, 8597, 9109, 9173, 9749, 9941, 10069, 10133, 10453
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007, Nov 12 2007

Keywords

Comments

All these primes are sums of two squares, also all indices are sums of two squares since we have the identity 64k+21 = 4(4(4k+1)+1)+1.

Crossrefs

Programs

  • Magma
    [p: p in PrimesUpTo(11000) | p mod 64 eq 21 ]; // Vincenzo Librandi, Sep 06 2012
  • Mathematica
    a = {}; Do[If[PrimeQ[21 + 64 n], AppendTo[a, 21 + 64 n]], {n, 0, 200}]; a
    Select[Prime[Range[1700]], MemberQ[{21}, Mod[#, 64]] &] (* Vincenzo Librandi, Sep 06 2012 *)

A127593 Primes of the form 256 k + 85.

Original entry on oeis.org

853, 1109, 1621, 1877, 2389, 3413, 5717, 6229, 6997, 7253, 10069, 10837, 11093, 12373, 13397, 16981, 17749, 18517, 18773, 19541, 21589, 22613, 23893, 24917, 27733, 29269, 30293, 31573, 32341, 37717, 39509, 40277, 41813, 43093, 46933
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[85 + 256 n], AppendTo[a, 85 + 256 n]], {n, 0, 200}]; a
    Select[256*Range[200]+85,PrimeQ] (* Harvey P. Dale, Oct 09 2020 *)

A127594 Numbers k such that 256 k + 85 is prime.

Original entry on oeis.org

3, 4, 6, 7, 9, 13, 22, 24, 27, 28, 39, 42, 43, 48, 52, 66, 69, 72, 73, 76, 84, 88, 93, 97, 108, 114, 118, 123, 126, 147, 154, 157, 163, 168, 183, 184, 186, 196, 198
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[85 + 256 n], AppendTo[a, n]], {n, 0, 200}]; a

A127597 Least number k such that k 4^n + (4^n-1)/3 is prime.

Original entry on oeis.org

2, 1, 0, 2, 3, 2, 4, 4, 3, 10, 3, 3, 2, 7, 2, 25, 6, 17, 4, 13, 3, 20, 36, 20, 11, 27, 66, 23, 39, 24, 19, 13, 3, 10, 6, 122, 71, 58, 24, 13, 3, 2, 41, 10, 6, 32, 58, 17, 4, 79, 26, 55, 36, 48, 31, 28, 9, 2, 76, 24, 32, 28, 63, 20, 37, 9, 2, 7, 39, 10, 91, 47
Offset: 0

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Programs

  • Mathematica
    a = {}; Do[k = 0; While[ !PrimeQ[k 4^n + (4^n - 1)/3], k++ ]; AppendTo[a, k], {n, 0, 50}]; a (*Artur Jasinski*)
    lnk[n_]:=Module[{k=0,n4=4^n},While[!PrimeQ[k*n4+(n4-1)/3],k++];k]; Array[ lnk,60,0] (* Harvey P. Dale, May 28 2018 *)
  • Python
    from sympy import isprime
    def a(n):
        k, fourn = 0, 4**n
        while not isprime(k*fourn + (fourn-1)//3): k += 1
        return k
    print([a(n) for n in range(72)]) # Michael S. Branicky, May 18 2022

Extensions

Offset corrected and a(51) and beyond from Michael S. Branicky, May 18 2022

A127598 Least primes of the form k 4^n + (4^n-1)/3.

Original entry on oeis.org

2, 5, 5, 149, 853, 2389, 17749, 70997, 218453, 2708821, 3495253, 13981013, 39146837, 492131669, 626349397, 27201459541, 27201459541, 297784399189, 297784399189, 3665038759253, 3665038759253, 89426945725781
Offset: 1

Views

Author

Artur Jasinski, Jan 19 2007

Keywords

Crossrefs

Programs

  • Mathematica
    a = {}; Do[k = 0; While[ !PrimeQ[k 4^n + (4^n - 1)/3], k++ ]; AppendTo[a, k 4^n + (4^n - 1)/3], {n, 0, 50}]; a (*Artur Jasinski*)

A153327 Numbers n such that 16*n+5 is not prime.

Original entry on oeis.org

1, 4, 5, 7, 8, 10, 13, 15, 16, 19, 20, 21, 22, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 43, 45, 46, 49, 50, 52, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 67, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 82, 83, 84, 85, 87, 88, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100
Offset: 1

Views

Author

Vincenzo Librandi, Dec 23 2008

Keywords

Examples

			Distribution of the terms in the following triangular array:
*;
*,*;
1,*,*;
*,*,*,*;
*,*,*,*,*,;
*,*,*,7,*,*;
*,*,*,*,10,*,*;
*,5,*,*,*,*,*,*;
*,*,8,*,*,*,*,*,*;
*,*,*,*,*,*,*,22,*,*;
4,*,*,*,*,*,*,*,27*,*;
*,*,*,*,*,20,*,*,*,*,*,*;
*,*,*,*,*,*,25,*,*,*,*,*,*; etc.
where * marks the non-integer values of (2*h*k + k + h - 2)/8 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013
		

Crossrefs

Cf. A127590.

Programs

  • Magma
    [n: n in [0..150] | not IsPrime(16*n + 5)]; // Vincenzo Librandi, Jan 12 2013
  • Mathematica
    Select[Range[100], !PrimeQ[16# + 5]&] (* Harvey P. Dale, Oct 03 2011 *)
Showing 1-7 of 7 results.