cp's OEIS Frontend

A385245 Primes that are no longer prime if in their binary representation any single bit is flipped but stay prime if a 1 bit is prepended.

%I A385245 #21 Aug 05 2025 06:07:55
%S A385245 223,257,509,787,853,877,1259,1451,1973,2917,3511,5099,6287,6521,7841,
%T A385245 8171,8923,9319,10567,11353,12517,12637,12763,13687,14107,14629,15217,
%U A385245 15607,16943,17519,18089,18593,18743,19139,20183,20393,20639,21701,22943,26591,26891
%N A385245 Primes that are no longer prime if in their binary representation any single bit is flipped but stay prime if a 1 bit is prepended.
%H A385245 Alois P. Heinz, <a href="/A385245/b385245.txt">Table of n, a(n) for n = 1..10000</a>
%F A385245 { A137985 } minus { A065092 }.
%e A385245 257 = 100000001_2 and 769 = 1100000001_2 are primes and 256, 259, 261, 265, 273, 289, 321, 385, 1 are not prime. So 257 is a term.
%p A385245 q:= p-> (m-> andmap(isprime, [p, 2^(m+1)+p]) and not ormap
%p A385245         (i->isprime(Bits[Xor](p, 2^i)), [$0..m]))(ilog2(p)):
%p A385245 select(q, [$2..27000])[];
%t A385245 Select[Prime[Range[3000]], PrimeQ[2^BitLength[#] + #] && NoneTrue[BitXor[#, 2^Range[0, BitLength[#] - 1]], PrimeQ] &] (* _Paolo Xausa_, Aug 05 2025 *)
%Y A385245 Set difference of A137985 and A065092.
%Y A385245 Cf. A000040, A002808.
%K A385245 nonn,base
%O A385245 1,1
%A A385245 _Alois P. Heinz_, Jul 28 2025