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
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..5590
Crossrefs
Cf. A365512.
Programs
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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;
Comments