A127575 -id:A127575 - cp's OEIS frontend

A127590 Numbers n such that 16n+5 is prime.

0, 2, 3, 6, 9, 11, 12, 14, 17, 18, 23, 24, 26, 38, 41, 42, 44, 47, 48, 51, 53, 62, 63, 66, 68, 69, 77, 81, 86, 89, 93, 101, 102, 104, 108, 116, 117, 123, 128, 129, 138, 143, 144, 146, 147, 149, 152, 159, 167, 168, 171, 174, 177, 182, 191, 194

Offset: 1

Artur Jasinski, Jan 19 2007

nonn

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589.

a = {}; Do[If[PrimeQ[16n + 5], AppendTo[a, n]], {n, 0, 200}]; a
Select[Range[0,200],PrimeQ[16#+5]&] (* Harvey P. Dale, Aug 31 2020 *)

is(n)=isprime(16*n+5) \\ Charles R Greathouse IV, Feb 17 2017

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

Artur Jasinski, Jan 19 2007

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127592, A127593, A127594.

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

Artur Jasinski, Jan 19 2007, Nov 12 2007

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.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127593, A127594.

[p: p in PrimesUpTo(11000) | p mod 64 eq 21 ]; // Vincenzo Librandi, Sep 06 2012

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 *)

A127579 Primes of the form 64n+63.

Original entry on oeis.org

127, 191, 383, 1087, 1151, 1279, 1471, 1663, 2111, 2239, 2687, 2879, 3391, 3583, 3967, 4159, 4799, 5119, 5503, 6079, 6143, 6271, 6719, 6911, 7039, 7103, 7487, 8191, 8447, 8831, 9151, 9343, 9791, 10111, 10303, 10559, 10687, 11071, 11519, 11839

Offset: 1

Artur Jasinski, Jan 19 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A127575, A127576, A127577, A127578, A127580, A127581.

[p: p in PrimesUpTo(12000) | p mod 64 eq 63]; // Vincenzo Librandi, Aug 25 2012

a = {}; Do[If[PrimeQ[64n + 63], AppendTo[a, 64n + 63]], {n, 1, 200}]; a
Select[Prime[Range[4000]], MemberQ[{63}, Mod[#, 64]] &] (* Vincenzo Librandi, Aug 25 2012 *)
Select[Range[63,12000,64],PrimeQ] (* Harvey P. Dale, Mar 01 2015 *)

forprime(p=2,1e6,if(bitand(p,63)==63,print1(p", "))) \\ Charles R Greathouse IV, May 15 2013

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

Artur Jasinski, Jan 19 2007

nonn

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127594.

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

Artur Jasinski, Jan 19 2007

nonn

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127593.

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

A127582 a(n) = the smallest prime number of the form k*2^n - 1, for k >= 1.

Original entry on oeis.org

2, 3, 3, 7, 31, 31, 127, 127, 1279, 3583, 5119, 6143, 8191, 8191, 81919, 131071, 131071, 131071, 524287, 524287, 14680063, 14680063, 109051903, 109051903, 654311423, 738197503, 738197503, 2147483647, 2147483647, 2147483647

Offset: 0

Artur Jasinski, Jan 19 2007

nonn

			a(0)=2 because 2 = 3*2^0 - 1 is prime.
a(1)=3 because 3 = 2*2^1 - 1 is prime.
a(2)=3 because 3 = 1*2^2 - 1 is prime.
a(3)=7 because 7 = 1*2^3 - 1 is prime.
a(4)=31 because 31 = 2*2^4 - 1 is prime.

Robert Israel, Table of n, a(n) for n = 0..3310

Cf. A007522, A127575-A127581, A127583-A127587.

A087522 is identical except for a(1).

p:= 2: A[0]:= 2:
for n from 1 to 100 do
  if p+1 mod 2^n = 0 then A[n]:= p
  else
    p:=p+2^(n-1);
    while not isprime(p) do p:= p+2^n od:
    A[n]:= p;
  fi
od:
seq(A[i],i=0..100); # Robert Israel, Jan 13 2017

a = {}; Do[k = 0; While[ !PrimeQ[k 2^n + 2^n - 1], k++ ]; AppendTo[a, k 2^n + 2^n - 1], {n, 0, 50}]; a (* Artur Jasinski, Jan 19 2007 *)

a(n) << 37^n by Xylouris's improvement to Linnik's theorem. - Charles R Greathouse IV, Dec 10 2013

Edited by Don Reble, Jun 11 2007

Further edited by N. J. A. Sloane, Jul 03 2008

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

Artur Jasinski, Jan 19 2007

nonn

Michael S. Branicky, Table of n, a(n) for n = 0..2391

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127593, A127594, A127598.

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 *)

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

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

Artur Jasinski, Jan 19 2007

nonn

Cf. A035050, A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127586, A127587, A127589, A127590, A127591, A127592, A127593, A127594, A127597.

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*)

A153264 Numbers n such that 16*n+15 is not prime.

Original entry on oeis.org

0, 3, 5, 6, 8, 9, 10, 12, 15, 17, 18, 19, 20, 21, 24, 25, 27, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 65, 66, 69, 70, 72, 73, 74, 75, 77, 78, 80, 81, 83, 84, 85, 86, 87, 90, 93, 94, 95, 96, 99

Offset: 1

Vincenzo Librandi, Dec 22 2008

			Distribution of the terms in the following triangular array:
*;
0,*;
*,*,*;
*,*,3,*;
*,*,*,*,*;
*,*,*,*,8,*;
*,*,*,*,*,*,*;
*,*,*,*,*,*,15,*;
*,5,*,*,*,*,*,*,*;
3,*,*,*,*,*,*,*,24,*;
*,*,*,12,*,*,*,*,*,*,*;
*,*,10,*,*,*,*,*,*,*,35,*; etc.
where * marks the non-integer values of (2*h*k + k + h - 7)/8 with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A127575.

[n: n in [0..150] | not IsPrime(16*n+15)]; // Vincenzo Librandi, Jan 12 2013

Select[Range[0, 200], !PrimeQ[16 # + 15] &] (* Vincenzo Librandi, Jan 12 2013 *)

0 added by Arkadiusz Wesolowski, Aug 03 2011

cp's OEIS Frontend

A127590 Numbers n such that 16n+5 is prime.

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

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A127592 Primes of the form 64k+21.

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A127579 Primes of the form 64n+63.

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A127593 Primes of the form 256 k + 85.

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

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A127582 a(n) = the smallest prime number of the form k*2^n - 1, for k >= 1.

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

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

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