A355273 - OEIS

%I #9 Jul 03 2022 09:18:41

%S 3,5,29,31,53,59,61,73,89,137,139,149,151,157,173,179,181,191,239,241,

%T 251,257,263,269,271,283,293,331,337,347,359,367,373,389,409,419,421,

%U 431,433,449,509,523,541,547,557,563,569,571,577,587,593,599,601,607,631

%N Primes p for which p + q is a multiple of 4, where q is the previous prime if p == 2 (mod 3) or the next prime otherwise.

%C Naively one might expect p + precprime / nextprime congruent to 0 or to 2 (mod 4) with equal probability. It turns out that, following the given rule, the case 2 is much more frequent than the case 0, especially for small primes. (Observation by Y. Kohmoto.)

%C See the comment from 2017 in A068228 for an explanation.

%o (PARI) select( is(p)=if(p%3==2, precprime(p-1)+p, nextprime(p+1)+p)%4==0, primes(149))

%o (Python)

%o from sympy import nextprime

%o from itertools import islice

%o def agen():

%o     p, q = 2, [3, 1]

%o     while True:

%o         if (p + q[int(p%3 == 2)])%4 == 0: yield p

%o         p, q = q[0], [nextprime(q[0]), p]

%o print(list(islice(agen(), 54))) # _Michael S. Branicky_, Jun 26 2022

%Y Cf. A151799 (previous prime), A151800 (next prime).

%Y Cf. A068228.

%K nonn

%O 1,1

%A _M. F. Hasler_ and _Yasutoshi Kohmoto_, Jun 26 2022