A161387 -id:A161387 - cp's OEIS frontend

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

Leroy Quet, Jun 08 2009

			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.

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

Cf. A161387.

[ 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

(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 *)

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

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

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

A229086 Numbers k such that the concatenation of the divisors of k written in base 2 is a palindromic number.

Original entry on oeis.org

1, 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

Jaroslav Krizek, Sep 13 2013

Concatenation of the divisors of n written in base 2 = A182621.
Are there composite numbers with this property?
Conjecture: a(n) for n > 1 is not equal to A161387, sequence also contains composites.
The answer to the question above is Yes. The first two composites are 297883 and 476635. - T. D. Noe, Sep 17 2013

			The number 103 is in sequence because the concatenation of its divisors written in base 2 (1, 1100111) is palindromic number - 11100111.

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

Cf. A161387, A182621.

Select[Range[10000], (temp=Flatten[IntegerDigits[Divisors[#],2]]; temp==Reverse[temp])&]

cp's OEIS Frontend

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

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