A127580 -id:A127580 - cp's OEIS frontend

A127579 Primes of the form 64n+63.

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

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*)

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

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Extensions

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

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Mathematica