A323784 Prime numbers such that the reverse of the balanced ternary representation is neither prime nor a negated prime.

3, 19, 23, 41, 47, 67, 79, 97, 107, 109, 113, 127, 131, 151, 157, 167, 191, 197, 211, 227, 229, 239, 251, 257, 271, 281, 283, 293, 307, 317, 337, 349, 359, 397, 409, 419, 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

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Github, Python code repository

Rosetta Code, Balanced Ternary Code

Wikipedia, Balanced Ternary

Example

79 is a term:
79 is +00-+ in balanced ternary notation
+00-+ reversed is +-00+
+-00+ is 55 in balanced ternary notation
55 prime factors are 5 and 11
Therefore 55 is not prime.
Therefore the prime number 79 "warps" to the nonprime number 55.
This operation is reversible: 55 "warps" to 79.

Prog

(Python) See links
(PARI) d3(n) = if ((n%3)==2, n\3+1, n\3);
m3(n) = if ((n%3)==2, -1, n % 3);
t(n) = if (n==0, [0], if (abs(n) == 1, [n], concat(m3(n), t(d3(n)))));
f(n) = subst(Pol(Vec(t(n))), x, 3);
isok(n) = isprime(n) && !isprime(abs(f(n))); \\ Michel Marcus, Jan 29 2019

Crossrefs

Cf. A134028, A323782.

Complement of A323782 among primes.

Sequence in context: A191074 A019408 A070045 * A063557 A197541 A273367

Adjacent sequences: A323781 A323782 A323783 * A323785 A323786 A323787

Keyword

nonn,base

Author

Philippe Cochin, Jan 28 2019

Status

approved