A161388 (Odd) binary palindromes n such that 2*n + 1 is a prime.

1, 3, 5, 9, 15, 21, 33, 51, 63, 65, 99, 119, 153, 165, 189, 219, 231, 273, 341, 443, 455, 495, 561, 585, 645, 765, 771, 891, 975, 1365, 1421, 1533, 1539, 1755, 1911, 2049, 2553, 2661, 2709, 2829, 2925, 3075, 3171, 3339, 3435, 3483, 3579, 4095, 4433, 4529

Offset: 1

Author

Leroy Quet, Jun 08 2009

Keywords

• base
• nonn

Examples

			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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..8639

Crossrefs

Cf. A161387.

Programs

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

Mathematica

(Select[Prime@Range[2,1500],(id=IntegerDigits[(#-1)/2,2]) == Reverse[id]&]-1)/2 (* Ray Chandler, Jun 09 2009*)
fQ[n_] := Block[{id = IntegerDigits[n, 2]}, id == Reverse@ id]; Select[ Range@ 4592, fQ@# && PrimeQ[2 # + 1] &] (* Robert G. Wilson v, Jun 09 2009 *)

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

Formula

a(n) = (A161387(n) - 1)/2.

Extensions

Extended by Hagen von Eitzen, Ray Chandler, Klaus Brockhaus and Robert G. Wilson v, Jun 09 2009