A214588 Primes p such that p mod 16 < 8.

2, 3, 5, 7, 17, 19, 23, 37, 53, 67, 71, 83, 97, 101, 103, 113, 131, 149, 151, 163, 167, 179, 181, 193, 197, 199, 211, 227, 229, 241, 257, 263, 277, 293, 307, 311, 337, 353, 359, 373, 389, 401, 419, 421, 433, 439, 449, 467, 487, 499, 503, 547, 563, 577, 593, 599

Offset: 1

Author

Brad Clardy, Jul 22 2012

Keywords

• nonn

Comments

Original definition: Primes p such that p XOR 8 = p + 8.

This is an example of a class of primes p such that p XOR n = p + n.

A002144 is the case where n=2, there are no cases where n=3, in A033203 n=4, 2 is the only p for n=5, in A007519 n=6, there are no cases where n=7. This sequence occurs when n=8.

In general if n is an odd number in A004767 there are no primes, if n is an odd number in A016813, then 2 is the only prime, and if n is an even number (A005843) there is a set of primes that satisfies the relationship p XOR n = p + n.

Examples

			103 is in the sequence because 103 mod 16 is 7 which is less than 8. - _Indranil Ghosh_, Jan 18 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A033203, A007519, A004767, A016813, A005843.

Programs

Magma

XOR := func;
for n in [2 .. 1000] do
   if IsPrime(n)  then  pn:=n;
      if (XOR(pn,8) eq pn+8) then pn; end if;
   end if;
end for;

Mathematica

Select[Prime[Range[200]],Mod[#,16]<8&] (* Harvey P. Dale, Jan 11 2018 *)

PARI

is_A214588(p)={ !bittest(p,3) & isprime(p) } \\ M. F. Hasler, Jul 24 2012

PARI

forprime(p=1,699, bittest(p,3) || print1(p",")) \\ M. F. Hasler, Jul 24 2012

Python

from sympy import isprime
i=1
while i<=600:
    if  isprime(i)==True and (i%16)<8:
        print(i, end=", ")
    i+=1 # Indranil Ghosh, Jan 18 2017