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A214588 Primes p such that p mod 16 < 8. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

(MAGMA)

XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)

                       where adigs := Intseq(a, 2, n)

                       where bdigs := Intseq(b, 2, n)

                       where n := 1 + Ilog2(Max([a, b, 1]))>;

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;

(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

j=1

while j<=10000:

....if  isprime(i)==True and (i%16)<8:

........print str(j)+" "+str(i)

........j+=1

....i+=1 # Indranil Ghosh, Jan 18 2017

CROSSREFS

Cf. A022144, A033203, A007519, A004767, A016813, A005843.

Sequence in context: A108222 A090725 A276141 * A089968 A164060 A113029

Adjacent sequences:  A214585 A214586 A214587 * A214589 A214590 A214591

KEYWORD

nonn

AUTHOR

Brad Clardy, Jul 22 2012

STATUS

approved

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Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)