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Primes p such that there is no power of 3 in the open interval (2p, 3p).
0

%I #16 Oct 20 2014 17:15:17

%S 5,7,17,19,23,41,43,47,53,59,61,67,71,73,79,127,131,137,139,149,151,

%T 157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,

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

%C Is this (apart from 2) the subset of primes in A134026? - _R. J. Mathar_, Sep 17 2012

%H Christian Salas, <a href="http://arxiv.org/abs/1203.3969">Cantor Primes as Prime-Valued Cyclotomic Polynomials</a>, arXiv preprint arXiv:1203.3969, 2012.

%p isA216731 := proc(n)

%p if isprime(n) then

%p floor(log[3](2*n)) = floor(log[3](3*n)) ;

%p else

%p false;

%p end if;

%p end proc:

%p for n from 2 to 250 do

%p p := ithprime(n) ;

%p if isA216731(p) then

%p printf("%d,",p) ;

%p end if;

%p end do: # _R. J. Mathar_, Sep 17 2012

%t 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 nonn

%O 1,1

%A _N. J. A. Sloane_, Sep 17 2012