A365518 - OEIS

%I #9 Sep 08 2023 13:18:46

%S 3,5,17,73,257,521,577,1033,1153,2081,2113,4129,16417,18433,32801,

%T 32833,65537,74017,133121,147457,262153,262433,262657,270337,270601,

%U 271393,295937,524353,524801,525313,532489,1048609,1049089,1056833,1065089,1082369,1179649,1183753,2101249,2367553,4194433

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

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

%H Robert Israel, <a href="/A365518/b365518.txt">Table of n, a(n) for n = 1..5590</a>

%e 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.

%p R:= NULL:

%p S[1]:= {1};

%p for d from 2 to 30 do

%p   S[d]:= {};

%p   for m from 1 to d-1 do

%p     for x in S[m] do

%p       y:= x + 2^(d-1);

%p       flag:= false;

%p       for j from 1 to m do

%p         w:= floor(y/2^j);

%p         if w::odd and isprime(w) then flag:= true; break fi;

%p       od;

%p       if flag then next fi;

%p       if isprime(y) then R:= R,y

%p       else S[d]:= S[d] union {y}

%p       fi

%p od od od:

%p R;

%Y Cf. A365512.

%K nonn,base

%O 1,1

%A _Robert Israel_, Sep 07 2023