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Quiteprimes: numbers k such that |2*(k mod p) - p| <= p + 1 - sqrt(p) for all primes p <= sqrt(k).
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%I #18 Aug 11 2021 20:17:46

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,137,139,149,151,157,163,167,173,179,191,

%U 193,211,223,227,229,239,251,257,269,271,277,281,283,293,317,347,349

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Quiteprime.html">Quiteprime</a>

%o (Python)

%o from math import isqrt

%o from sympy import primerange

%o def ok(n):

%o if n < 2: return False

%o for p in primerange(2, isqrt(n)+1):

%o isqrtp = isqrt(p)

%o if abs(2*(n%p)-p) > p + 1 - isqrt(p) - (isqrtp**2 < p): return False

%o return True

%o print(list(filter(ok, range(2, 350)))) # _Michael S. Branicky_, Aug 11 2021

%Y Cf. A050261.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Jim Ferry (jferry(AT)uiuc.edu)

%E Title improved by _Sean A. Irvine_, Aug 11 2021