A216731 Primes p > 3 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

Author

N. J. A. Sloane, Sep 17 2012

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Christian Salas, Cantor Primes as Prime-Valued Cyclotomic Polynomials, arXiv preprint arXiv:1203.3969 [math.NT], 2012.

Programs

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 *)

Extensions

Name corrected by Robert Israel, May 11 2025