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

1,1

Links

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

Formula

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

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, it is in this sequence.

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 *)

Prog

(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
(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

Crossrefs

Cf. A161388.

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

Sequence in context: A202301 A339974 A123080 * A229086 A354902 A022406

Adjacent sequences: A161384 A161385 A161386 * A161388 A161389 A161390

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