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

5, 7, 17, 19, 23, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 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

Offset

1,1

Comments

Is this (apart from 2) the subset of primes in A134026? - R. J. Mathar, Sep 17 2012

Links

Table of n, a(n) for n=1..63.

Christian Salas, Cantor Primes as Prime-Valued Cyclotomic Polynomials, arXiv preprint arXiv:1203.3969, 2012.

Maple

isA216731 := proc(n)
    if isprime(n) then
        floor(log[3](2*n)) = floor(log[3](3*n)) ;
    else
        false;
    end if;
end proc:
for n from 2 to 250 do
     p := ithprime(n) ;
    if isA216731(p) then
        printf("%d, ", p) ;
    end if;
end do: # R. J. Mathar, Sep 17 2012

Mathematica

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 *)

Crossrefs

Sequence in context: A140564 A253085 A078764 * A363752 A045318 A040102

Adjacent sequences: A216728 A216729 A216730 * A216732 A216733 A216734

Keyword

nonn

Author

N. J. A. Sloane, Sep 17 2012

Status

approved