A355272 Primes p for which p + q is not a multiple of 4, where q is the previous prime if p == 1 (mod 3) or else the next prime.

2, 89, 97, 211, 223, 359, 367, 389, 397, 401, 409, 449, 457, 467, 479, 487, 491, 499, 509, 631, 673, 683, 691, 701, 709, 719, 727, 743, 751, 761, 769, 797, 887, 907, 911, 919, 929, 937, 983, 991, 1009, 1109, 1117, 1163, 1171, 1193, 1201, 1213, 1249, 1307, 1373

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 0 is much more frequent than the case 2, 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..51.

Prog

(PARI) select( is(p)=if(p%3==1, precprime(p-1)+p, nextprime(p+1)+p)%4, primes(199))
(Python)
from sympy import nextprime
from itertools import islice
def agen():
    p, q = 2, [3, 1]
    while True:
        if (p + q[int(p%3 == 1)])%4 != 0: yield p
        p, q = q[0], [nextprime(q[0]), p]
print(list(islice(agen(), 51))) # Michael S. Branicky, Jun 26 2022

Crossrefs

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

Cf. A068228.

Sequence in context: A012728 A012733 A058459 * A105268 A139881 A161676

Adjacent sequences: A355269 A355270 A355271 * A355273 A355274 A355275

Keyword

nonn

Author

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

Status

approved