A355273 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.

3, 5, 29, 31, 53, 59, 61, 73, 89, 137, 139, 149, 151, 157, 173, 179, 181, 191, 239, 241, 251, 257, 263, 269, 271, 283, 293, 331, 337, 347, 359, 367, 373, 389, 409, 419, 421, 431, 433, 449, 509, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 631

Offset

1,1

Comments

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.)

See the comment from 2017 in A068228 for an explanation.

Links

Table of n, a(n) for n=1..55.

Prog

(PARI) select( is(p)=if(p%3==2, precprime(p-1)+p, nextprime(p+1)+p)%4==0, primes(149))
(Python)
from sympy import nextprime
from itertools import islice
def agen():
    p, q = 2, [3, 1]
    while True:
        if (p + q[int(p%3 == 2)])%4 == 0: yield p
        p, q = q[0], [nextprime(q[0]), p]
print(list(islice(agen(), 54))) # Michael S. Branicky, Jun 26 2022

Crossrefs

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

Cf. A068228.

Sequence in context: A300676 A016552 A321069 * A361085 A141578 A327748

Adjacent sequences: A355270 A355271 A355272 * A355274 A355275 A355276

Keyword

nonn

Author

M. F. Hasler and Yasutoshi Kohmoto, Jun 26 2022

Status

approved