A365518 Odd primes whose base-2 representation has no proper substrings that are base-2 representations of odd primes.

3, 5, 17, 73, 257, 521, 577, 1033, 1153, 2081, 2113, 4129, 16417, 18433, 32801, 32833, 65537, 74017, 133121, 147457, 262153, 262433, 262657, 270337, 270601, 271393, 295937, 524353, 524801, 525313, 532489, 1048609, 1049089, 1056833, 1065089, 1082369, 1179649, 1183753, 2101249, 2367553, 4194433

Offset

1,1

Comments

All terms of A365512 are terms of this sequence. The first term that does not occur in A365512 appears to be 521.

Links

Robert Israel, Table of n, a(n) for n = 1..5590

Example

a(4) = 73 is a term because 73 is an odd prime, its binary representation is 1001001, and no proper substring of 1001001 is the binary representation of an odd prime.

Maple

R:= NULL:
S[1]:= {1};
for d from 2 to 30 do
  S[d]:= {};
  for m from 1 to d-1 do
    for x in S[m] do
      y:= x + 2^(d-1);
      flag:= false;
      for j from 1 to m do
        w:= floor(y/2^j);
        if w::odd and isprime(w) then flag:= true; break fi;
      od;
      if flag then next fi;
      if isprime(y) then R:= R, y
      else S[d]:= S[d] union {y}
      fi
od od od:
R;

Crossrefs

Cf. A365512.

Sequence in context: A356256 A232238 A102295 * A227335 A351718 A281627

Adjacent sequences: A365515 A365516 A365517 * A365519 A365520 A365521

Keyword

nonn,base

Author

Robert Israel, Sep 07 2023

Status

approved