A323782 -id:A323782 - cp's OEIS frontend

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

Philippe Cochin, Jan 27 2019

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

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

			-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.

Corresponding warp prime numbers to A323782.

Supersequence of A224502.

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

Python
```
# See Github link.
```

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

Original entry on oeis.org

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

Philippe Cochin, Jan 28 2019

			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.

Cf. A134028, A323782.

Complement of A323782 among primes.

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

Python
```
# See Github link.
```

cp's OEIS Frontend

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

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