A323783 a(n) = A134028(A323782(n)): Primes and negated primes such that the reverse of the balanced ternary representation is a prime.

-2, -11, 7, -5, 13, -29, -17, 37, 31, 43, -83, -101, 61, -89, 73, -53, -71, -59, 103, -173, 313, -353, 241, -137, -263, 223, 331, 277, 181, -269, 163, -179, -233, 199, -347, 139, 193, -311, -149, 367, 853, 691, -929, -443, -983, 421, -389, -839, 457, -677

Offset

1,1

Comments

The "warp" operation is reversible between A323782 and this sequence.

Negating a number in balanced ternary notation is done by inverting the + and -.

Links

Table of n, a(n) for n=1..50.

Github, Python code repository

Rosetta Code, Balanced Ternary Code

Wikipedia, Balanced Ternary

Example

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

Prog

(Python) # See Github link.
(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);
lista(nn) = {forprime(n=1, nn, if (isprime(abs(f(n))), print1(f(n), ", ")); ); } \\ Michel Marcus, Jan 29 2019

Crossrefs

Corresponding warp prime numbers to A323782.

Supersequence of A224502.

Sequence in context: A226219 A285866 A165768 * A306537 A170873 A224210

Adjacent sequences: A323780 A323781 A323782 * A323784 A323785 A323786

Keyword

sign,base,changed

Author

Philippe Cochin, Jan 27 2019

Status

approved