cp's OEIS Frontend

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.

%I A092570 #15 Jul 16 2025 15:24:25
%S A092570 2,3,5,7,11,13,17,19,29,31,37,43,53,59,79,83,89,103,109,113,151,157,
%T A092570 173,191,193,211,227,233,269,277,281,307,311,337,347,349,359,367,379,
%U A092570 389,401,409,419,421,431,457,461,487,491,499,523,569,599,607,617,653,659
%N 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.
%H A092570 Harvey P. Dale, <a href="/A092570/b092570.txt">Table of n, a(n) for n = 1..1000</a>
%e A092570 307 and 461 are terms because 307_10 = 100110011_2, transformation of inner bits gives 100110011_2 -> 111001101_2 = 461_10.
%t A092570 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 *)
%o A092570 (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)};
%o A092570 forprime(p=2,659,if(isprime(T(p)),print1(p,", ")))
%o A092570 \\ _Washington Bomfim_, Jan 18 2011
%Y A092570 Cf. A092569.
%K A092570 base,nonn,easy
%O A092570 1,1
%A A092570 _Zak Seidov_, Feb 28 2004