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

1,2

Links

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

Formula

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A161387.

Sequence in context: A029470 A323646 A182185 * A229552 A029518 A061954

Adjacent sequences: A161385 A161386 A161387 * A161389 A161390 A161391

Keyword

base,nonn

Author

Leroy Quet, Jun 08 2009

Extensions

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

Status

approved