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A216731 Primes p > 3 such that there is no power of 3 in the open interval (2p, 3p).

%I A216731 #23 May 12 2025 14:37:08
%S A216731 5,7,17,19,23,41,43,47,53,59,61,67,71,73,79,127,131,137,139,149,151,
%T A216731 157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,
%U A216731 367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509
%N A216731 Primes p > 3 such that there is no power of 3 in the open interval (2p, 3p).
%C A216731 Is this (apart from 2) the subset of primes in A134026? - _R. J. Mathar_, Sep 17 2012
%H A216731 Robert Israel, <a href="/A216731/b216731.txt">Table of n, a(n) for n = 1..10000</a>
%H A216731 Christian Salas, <a href="http://arxiv.org/abs/1203.3969">Cantor Primes as Prime-Valued Cyclotomic Polynomials</a>, arXiv preprint arXiv:1203.3969 [math.NT], 2012.
%p A216731 isA216731 := proc(n)
%p A216731     if isprime(n) then
%p A216731         floor(log[3](2*n)) = floor(log[3](3*n)) ;
%p A216731     else
%p A216731         false;
%p A216731     end if;
%p A216731 end proc:
%p A216731 for n from 2 to 250 do
%p A216731     p := ithprime(n) ;
%p A216731     if isA216731(p) then
%p A216731         printf("%d,",p) ;
%p A216731     end if;
%p A216731 end do: # _R. J. Mathar_, Sep 17 2012
%t A216731 isA216731[n_] := If[PrimeQ[n], Floor[Log[3, 2*n]] == Floor[Log[3, 3*n]], False]; Reap[For[n = 2, n <= 100, n++, p = Prime[n]; If[isA216731[p], Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Mar 06 2014, after _R. J. Mathar_ *)
%K A216731 nonn
%O A216731 1,1
%A A216731 _N. J. A. Sloane_, Sep 17 2012
%E A216731 Name corrected by _Robert Israel_, May 11 2025