A092570 Primes p which become a prime q under transformation of inner bits of binary representation in A092569. In binary representation of p, transformation of inner bits, 1 <-> 0, gives binary representation of q.

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 43, 53, 59, 79, 83, 89, 103, 109, 113, 151, 157, 173, 191, 193, 211, 227, 233, 269, 277, 281, 307, 311, 337, 347, 349, 359, 367, 379, 389, 401, 409, 419, 421, 431, 457, 461, 487, 491, 499, 523, 569, 599, 607, 617, 653, 659

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

307 and 461 are terms because 307_10 = 100110011_2, transformation of inner bits gives 100110011_2 -> 111001101_2 = 461_10.

Mathematica

ptibQ[n_]:=Module[{id=IntegerDigits[n, 2], f, l, r}, f=id[[1]]; l=id[[-1]]; r=Most[Rest[id]]; PrimeQ[FromDigits[Join[{f}, r/.{1->0, 0->1}, {l}], 2]]]; Select[Prime[Range[200]], ptibQ] (* Harvey P. Dale, Jul 16 2025 *)

Prog

(PARI)T(p)={pow2=2; v=binary(p); L=#v-1; forstep(k=L, 2, -1, if(v[k], p-=pow2, p+=pow2); pow2*=2); return(p)};
forprime(p=2, 659, if(isprime(T(p)), print1(p, ", ")))
\\ Washington Bomfim, Jan 18 2011

Crossrefs

Cf. A092569.

Sequence in context: A174144 A104885 A127052 * A133956 A176164 A141409

Adjacent sequences: A092567 A092568 A092569 * A092571 A092572 A092573

Keyword

base,nonn,easy

Author

Zak Seidov, Feb 28 2004

Status

approved