cp's OEIS Frontend

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.

%I A355272 #13 Jul 03 2022 09:18:15
%S A355272 2,89,97,211,223,359,367,389,397,401,409,449,457,467,479,487,491,499,
%T A355272 509,631,673,683,691,701,709,719,727,743,751,761,769,797,887,907,911,
%U A355272 919,929,937,983,991,1009,1109,1117,1163,1171,1193,1201,1213,1249,1307,1373
%N 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.
%C A355272 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.)
%C A355272 See the comment from 2017 in A068228 for an explanation.
%o A355272 (PARI) select( is(p)=if(p%3==1, precprime(p-1)+p, nextprime(p+1)+p)%4, primes(199))
%o A355272 (Python)
%o A355272 from sympy import nextprime
%o A355272 from itertools import islice
%o A355272 def agen():
%o A355272     p, q = 2, [3, 1]
%o A355272     while True:
%o A355272         if (p + q[int(p%3 == 1)])%4 != 0: yield p
%o A355272         p, q = q[0], [nextprime(q[0]), p]
%o A355272 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Jun 26 2022
%Y A355272 Cf. A151799 (previous prime), A151800 (next prime).
%Y A355272 Cf. A068228.
%K A355272 nonn
%O A355272 1,1
%A A355272 _M. F. Hasler_ and _Yasutoshi Kohmoto_, Jun 26 2022