login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323784 Prime numbers such that the reverse of the balanced ternary representation is neither prime nor a negated prime. 1

%I

%S 3,19,23,41,47,67,79,97,107,109,113,127,131,151,157,167,191,197,211,

%T 227,229,239,251,257,271,281,283,293,307,317,337,349,359,397,409,419,

%U 431,433,439,461,463,491,503,521,523,557,563,571,577,587,593,617,619,631,641,647,653,659,661,673,683,701,733,743,769,787,797

%N Prime numbers such that the reverse of the balanced ternary representation is neither prime nor a negated prime.

%H Github, <a href="https://github.com/sneakyweasel/WarpPrimes">Python code repository</a>

%H Rosetta Code, <a href="http://www.rosettacode.org/wiki/Balanced_ternary">Balanced Ternary Code</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>

%e 79 is a term:

%e 79 is +00-+ in balanced ternary notation

%e +00-+ reversed is +-00+

%e +-00+ is 55 in balanced ternary notation

%e 55 prime factors are 5 and 11

%e Therefore 55 is not prime.

%e Therefore the prime number 79 "warps" to the nonprime number 55.

%e This operation is reversible: 55 "warps" to 79.

%o (Python) See links

%o (PARI) d3(n) = if ((n%3)==2, n\3+1, n\3);

%o m3(n) = if ((n%3)==2, -1, n % 3);

%o t(n) = if (n==0, [0], if (abs(n) == 1, [n], concat(m3(n), t(d3(n)))));

%o f(n) = subst(Pol(Vec(t(n))), x, 3);

%o isok(n) = isprime(n) && !isprime(abs(f(n))); \\ _Michel Marcus_, Jan 29 2019

%Y Cf. A134028, A323782.

%Y Complement of A323782 among primes.

%K nonn,base

%O 1,1

%A _Philippe Cochin_, Jan 28 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)