[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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