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 A323782 Prime numbers such that the reverse of the balanced ternary representation is a prime or a negated prime. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The "warp" operation is an inverse map connecting this sequence and A323783. LINKS 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, , 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 >= 2, d-=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: A245063 A168033 A257974 * A020591 A197188 A265809 Adjacent sequences:  A323779 A323780 A323781 * A323783 A323784 A323786 KEYWORD nonn,base AUTHOR Philippe Cochin, Jan 27 2019 STATUS approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)