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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. 1

%I #29 Mar 26 2019 16:32:52

%S -2,-11,7,-5,13,-29,-17,37,31,43,-83,-101,61,-89,73,-53,-71,-59,103,

%T -173,313,-353,241,-137,-263,223,331,277,181,-269,163,-179,-233,199,

%U -347,139,193,-311,-149,367,853,691,-929,-443,-983,421,-389,-839,457,-677

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

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

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

%H Github, <a href="https://github.com/sneakyweasel/WarpPrimes">Python code repository</a>

%H Rosetta Code, <a href="http://www.rosettacode.org/wiki/Balanced_ternary">Balanced Ternary Code</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>

%e -17 is a term:

%e -17 is -+0+ in balanced ternary notation

%e -+0+ reversed is +0+-

%e +0+- is 29 in balanced ternary notation

%e 29 is prime

%e Therefore -17 is "warped" to 29.

%e This operation is reversible: 29 "warps" to -17.

%o (Python) See links

%o (PARI) d3(n) = if ((n%3)==2, n\3+1, n\3);

%o m3(n) = if ((n%3)==2, -1, n % 3);

%o t(n) = if (n==0, [0], if (abs(n) == 1, [n], concat(m3(n), t(d3(n)))));

%o f(n) = subst(Pol(Vec(t(n))), x, 3);

%o lista(nn) = {forprime(n=1, nn, if (isprime(abs(f(n))), print1(f(n), ", ")););} \\ _Michel Marcus_, Jan 29 2019

%Y Corresponding warp prime numbers to A323782.

%Y Supersequence of A224502.

%K sign,base

%O 1,1

%A _Philippe Cochin_, Jan 27 2019

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Last modified April 17 22:23 EDT 2024. Contains 371767 sequences. (Running on oeis4.)