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A365518
Odd primes whose base-2 representation has no proper substrings that are base-2 representations of odd primes.
1
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
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
KEYWORD
nonn,base
AUTHOR
Robert Israel, Sep 07 2023
STATUS
approved