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%I #20 Sep 08 2022 08:45:45
%S 1,3,5,9,15,21,33,51,63,65,99,119,153,165,189,219,231,273,341,443,455,
%T 495,561,585,645,765,771,891,975,1365,1421,1533,1539,1755,1911,2049,
%U 2553,2661,2709,2829,2925,3075,3171,3339,3435,3483,3579,4095,4433,4529
%N (Odd) binary palindromes n such that 2*n + 1 is a prime.
%H Chai Wah Wu, <a href="/A161388/b161388.txt">Table of n, a(n) for n = 1..8639</a>
%F a(n) = (A161387(n) - 1)/2.
%e 67 in binary is 1000011. All binary digits but the rightmost 1 form a palindrome (100001), so therefore (67-1)/2 = 33 is a palindrome. Since 67 is a prime, 33 is in this sequence.
%t (Select[Prime@Range[2,1500],(id=IntegerDigits[(#-1)/2,2]) == Reverse[id]&]-1)/2 (* _Ray Chandler_, Jun 09 2009*)
%t fQ[n_] := Block[{id = IntegerDigits[n, 2]}, id == Reverse@ id]; Select[ Range@ 4592, fQ@# && PrimeQ[2 # + 1] &] (* _Robert G. Wilson v_, Jun 09 2009 *)
%o (PARI) forprime(p=3,100000,t=binary((p-1)/2);if(t==vector(#t,x,t[ #t+1-x]),print1((p-1)/2,","))) \\ _Hagen von Eitzen_, Jun 10 2009
%o (Magma) [ n: p in PrimesInInterval(3, 9100) | s eq Reverse(s) where s is Intseq(n, 2) where n is (p-1) div 2]; // _Klaus Brockhaus_, Jun 09 2009
%Y Cf. A161387.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Jun 08 2009
%E Extended by _Hagen von Eitzen_, _Ray Chandler_, _Klaus Brockhaus_ and _Robert G. Wilson v_, Jun 09 2009
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