A050260 Quiteprimes: numbers k such that |2*(k mod p) - p| <= p + 1 - sqrt(p) for all primes p <= sqrt(k).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 163, 167, 173, 179, 191, 193, 211, 223, 227, 229, 239, 251, 257, 269, 271, 277, 281, 283, 293, 317, 347, 349

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Eric Weisstein's World of Mathematics, Quiteprime

Prog

(Python)
from math import isqrt
from sympy import primerange
def ok(n):
    if n < 2: return False
    for p in primerange(2, isqrt(n)+1):
        isqrtp = isqrt(p)
        if abs(2*(n%p)-p) > p + 1 - isqrt(p) - (isqrtp**2 < p): return False
    return True
print(list(filter(ok, range(2, 350)))) # Michael S. Branicky, Aug 11 2021

Crossrefs

Cf. A050261.

Sequence in context: A058853 A049569 A100725 * A095316 A095313 A095285

Adjacent sequences: A050257 A050258 A050259 * A050261 A050262 A050263

Keyword

nonn

Author

Eric W. Weisstein, Jim Ferry (jferry(AT)uiuc.edu)

Extensions

Title improved by Sean A. Irvine, Aug 11 2021

Status

approved