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

1,1

Links

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

Formula

{ A137985 } minus { A065092 }.

Example

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.

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 *)

Crossrefs

Set difference of A137985 and A065092.

Cf. A000040, A002808.

Sequence in context: A359449 A098591 A138665 * A271799 A152824 A142386

Adjacent sequences: A385242 A385243 A385244 * A385246 A385247 A385248

Keyword

nonn,base

Author

Alois P. Heinz, Jul 28 2025

Status

approved