The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117697 Palindromic primes in base 2 (written in base 2). 9
11, 101, 111, 10001, 11111, 1001001, 1101011, 1111111, 100000001, 100111001, 110111011, 10010101001, 10110101101, 11000100011, 11001010011, 11011111011, 11100100111, 11101010111, 1001100011001, 1001111111001, 1010001000101 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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.
FORMULA
a(n) = A007088(A016041(n)). - R. J. Mathar, Feb 25 2007
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 *)
CROSSREFS
Sequence in context: A350346 A247647 A240602 * A305395 A158051 A091366
KEYWORD
nonn,base
AUTHOR
Martin Renner, Apr 13 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)