A117697 Palindromic primes in base 2 (written in base 2).

11, 101, 111, 10001, 11111, 1001001, 1101011, 1111111, 100000001, 100111001, 110111011, 10010101001, 10110101101, 11000100011, 11001010011, 11011111011, 11100100111, 11101010111, 1001100011001, 1001111111001, 1010001000101

Offset: 1

Author

Martin Renner, Apr 13 2006

Keywords

• nonn
• base

Links

• Attila Olah, Table of n, a(n) for n=1..43964
• Lubomira Dvorakova, Stanislav Kruml, and David Ryzak, Antipalindromic numbers, arXiv:2008.06864 [math.CO], 2020. Mentions this sequence.
• Eric Weisstein's World of Mathematics, Palindromic Prime.

Crossrefs

Cf. A016041, A002385.

Programs

Maple

isA016041 := proc(n)
    local bin,dig ;
    if isprime(n) then
        bin := convert(n,base,2) ;
        for dig from 1 to nops(bin)/2 do
            if op(dig,bin) <> op(-dig,bin) then
                return false;
            end if;
        end do ;
        return true;
    else
        false ;
    end if ;
end proc:
for i from 1 to 900 do p := ithprime(i) : if isA016041(p) then printf("%d, ",A007088(p)) ; fi ; od : # R. J. Mathar, Feb 25 2007

Mathematica

pal2Q[n_] := Reverse[x = IntegerDigits[n, 2]] == x; BaseForm[Select[Prime[Range[700]], pal2Q[#] &], 2] (* Jayanta Basu, Jun 24 2013 *)
FromDigits /@ Select[IntegerDigits[Prime@ Range[1000], 2], PalindromeQ] (* Michael De Vlieger, Oct 28 2020 *)

Formula

a(n) = A007088(A016041(n)). - R. J. Mathar, Feb 25 2007