A397429 - OEIS

%I #14 Jul 07 2026 21:36:07

%S 11,23,37,43,47,67,71,83,131,151,163,167,173,199,223,263,269,277,283,

%T 307,331,349,359,383,431,463,479,521,571,599,601,619,631,643,653,661,

%U 683,691,701,727,739,823,827,839,911,1033,1049,1087,1091,1093,1109,1117

%N Primes in A161601 whose binary reversal is prime.

%H Vincenzo Librandi, <a href="/A397429/b397429.txt">Table of n, a(n) for n = 1..8237</a>

%e The pairs (A161601(k), A161603(k)) for k=1..5 are (11,13), (19,25), (23,29), (35,49), (37,41), so this sequence begins with 11,23,37.

%e For (37,41), we have (37 base 2) = 100101 and (41 base 2) = 10101, which is the reverse of 100101, as in A161601(5) and A161603(5).

%t p[f_] := Module[{n = 1, c = 0}, Reap[While[c < f, With[{d = IntegerDigits[n, 2]}, With[{r = Reverse[d]}, If[d =!= r && n < FromDigits[r, 2],

%t Sow[{n, FromDigits[r, 2]}]; c++]]]; n += 2]][[2, 1]]];

%t u = Select[p[300], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &];

%t Map[First, u]

%t (* _Peter J. C. Moses_, Jun 24 2026 *)

%Y Cf. A000040, A161601, A161603, A397430, A397431, A397432.

%K nonn,easy,base,new

%O 1,1

%A _Clark Kimberling_, Jun 24 2026