A161387 Primes p such that (p-1)/2 is an (odd) binary palindrome.

3, 7, 11, 19, 31, 43, 67, 103, 127, 131, 199, 239, 307, 331, 379, 439, 463, 547, 683, 887, 911, 991, 1123, 1171, 1291, 1531, 1543, 1783, 1951, 2731, 2843, 3067, 3079, 3511, 3823, 4099, 5107, 5323, 5419, 5659, 5851, 6151, 6343, 6679, 6871, 6967, 7159, 8191

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, it is in this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A161388.

Terms include A000668. - Robert G. Wilson v, Jun 09 2009

Programs

Magma

[ p: p in PrimesInInterval(3, 8200) | s eq Reverse(s) where s is Intseq((p-1) div 2, 2) ]; // Klaus Brockhaus, Jun 09 2009

Mathematica

Select[Prime@Range[2,1500],(id=IntegerDigits[(#-1)/2,2])==Reverse[id]&] (* Ray Chandler, Jun 09 2009 *)
fQ[n_] := Block[{id = IntegerDigits[(n - 1)/2, 2]}, id == Reverse@id]; Select[ Prime@ Range[2, 1100], fQ@# &] (* 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,","))) \\ Hagen von Eitzen, Jun 10 2009

Formula

a(n) = 2*A161388(n) + 1.

Extensions

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