A323782 Prime numbers such that the reverse of the balanced ternary representation is a prime or a negated prime.

2, 5, 7, 11, 13, 17, 29, 31, 37, 43, 53, 59, 61, 71, 73, 83, 89, 101, 103, 137, 139, 149, 163, 173, 179, 181, 193, 199, 223, 233, 241, 263, 269, 277, 311, 313, 331, 347, 353, 367, 373, 379, 383, 389, 401, 421, 443, 449, 457, 467, 479, 487, 499, 509, 541

Offset

1,1

Comments

The "warp" operation is an inverse map connecting this sequence and A323783.

Links

Table of n, a(n) for n=1..55.

Github, Python code repository

Rosetta Code, Balanced Ternary Code

Wikipedia, Balanced Ternary

Example

29 is a term:
29 is +0+- in balanced ternary notation
+0+- reversed is -+0+
-+0+ is -17 in balanced ternary notation
the absolute value of -17 is 17.
17 is prime
Therefore 29 is "warped" to -17.
This operation is reversible: -17 "warps" to 29.

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
(PARI) is(n) = {if(!isprime(n), return(0)); my(d = digits(n, 3)); forstep(i = #d, 2, -1, if(d[i] >= 2, d[i] -= 3; d[i-1]++)); if(d[1] >= 2, d[1]-=3; d = concat(1, d)); isprime(abs(fromdigits(Vecrev(d), 3)))} \\ David A. Corneth, Feb 14 2019

Crossrefs

Cf. A000040, A134028.

Supersequence of A224502.

Corresponding primes and -primes are in sequence A323783.

Primes that don't "warp" to a prime numbers are in sequence A323784.

Sequence in context: A168033 A331486 A257974 * A020591 A197188 A265809

Adjacent sequences: A323779 A323780 A323781 * A323783 A323784 A323785

Keyword

nonn,base

Author

Philippe Cochin, Jan 27 2019

Status

approved