A224502 -id:A224502 - cp's OEIS frontend

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

Philippe Cochin, Jan 27 2019

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

			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.

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.

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

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

Python
```
# See links.
```

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

Original entry on oeis.org

-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.
```

cp's OEIS Frontend

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

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python