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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