OFFSET

1,1

COMMENTS

There are primes p for which there exist a positive integer k and another prime q such that p=q*(2k+1)-2k. See A136020, A091180, A136061 and the subsequent sequences. Such k is called an "order" of the prime p. Note that q is necessarily larger than 2 and that 4*k is necessarily smaller than p-1. A prime may belong to more than one order, but the primes listed in the present sequence do not belong to any order.

As soon as they are larger than 8, all members minus 1 are multiples of 8.

MATHEMATICA

lim = 2000; p = 2; listc = {}; listp = {}; While[p < lim, n = 1;

While[n <= (p - 3)/4,

If[PrimeQ[(p + 2 n)/(2 n + 1)], n = 2*p, n = n + 1]];

If[n == 2*p, AppendTo[listc, p]]; AppendTo[listp, p];

p = NextPrime[p]]; Complement[listp, listc]

PROG

(PARI) isok(p) = {if (isprime(p), for (k=1, (p-3)/4, my(q = (p+2*k)/(2*k+1)); if ((denominator(q)==1) && isprime(q), return(0)); ); return (1); ); } \\ Michel Marcus, Oct 07 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

RenĂ© Gy, Oct 03 2021

EXTENSIONS

More terms from Michel Marcus, Oct 04 2021

STATUS

approved