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.

223, 257, 509, 787, 853, 877, 1259, 1451, 1973, 2917, 3511, 5099, 6287, 6521, 7841, 8171, 8923, 9319, 10567, 11353, 12517, 12637, 12763, 13687, 14107, 14629, 15217, 15607, 16943, 17519, 18089, 18593, 18743, 19139, 20183, 20393, 20639, 21701, 22943, 26591, 26891

Offset: 1

Author

Alois P. Heinz, Jul 28 2025

Keywords

• nonn
• base

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Set difference of A137985 and A065092.

Cf. A000040, A002808.

Programs

Maple

q:= p-> (m-> andmap(isprime, [p, 2^(m+1)+p]) and not ormap
        (i->isprime(Bits[Xor](p, 2^i)), [$0..m]))(ilog2(p)):
select(q, [$2..27000])[];

Mathematica

Select[Prime[Range[3000]], PrimeQ[2^BitLength[#] + #] && NoneTrue[BitXor[#, 2^Range[0, BitLength[#] - 1]], PrimeQ] &] (* Paolo Xausa, Aug 05 2025 *)

Formula

{ A137985 } minus { A065092 }.