

A163410


A positive integer is included if it is a palindrome when written in binary, and it is not divisible by any primes that are not binary palindromes.


3



1, 3, 5, 7, 9, 15, 17, 21, 27, 31, 45, 51, 63, 73, 85, 93, 107, 119, 127, 153, 189, 219, 255, 257, 313, 365, 381, 443, 511, 765, 771, 1193, 1241, 1285, 1453, 1533, 1571, 1619, 1787, 1799, 1831, 1879, 2313, 3579, 3855, 4369, 4889, 5113, 5189, 5397, 5557, 5869
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OFFSET

1,2


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

51 in binary is 110011, which is a palindrome. 51 is divisible by the primes 3 and 17. 3 in binary is 11, a palindrome. And 17 in binary is 10001, also a palindrome. Since all the primes dividing the binary palindrome 51 are themselves binary palindromes, then 51 is included in this sequence.


MAPLE

dmax:= 15: # to get all terms with at most dmax binary digits
revdigs:= proc(n)
local L, Ln, i;
L:= convert(n, base, 2);
Ln:= nops(L);
add(L[i]*2^(Lni), i=1..Ln);
end proc:
isbpali:= proc(n) option remember; local L; L:= convert(n, base, 2); L=ListTools:Reverse(L) end proc:
Bp:= {0, 1}:
for d from 2 to dmax do
if d::even then
Bp:= Bp union {seq(2^(d/2)*x + revdigs(x), x=2^(d/21)..2^(d/2)1)}
else
m:= (d1)/2;
B:={seq(2^(m+1)*x + revdigs(x), x=2^(m1)..2^m1)};
Bp:= Bp union B union map(`+`, B, 2^m)
fi
od:
R:= select(t > andmap(isbpali, numtheory:factorset(t)), Bp minus {0}):
sort(convert(R, list)); # Robert Israel, Dec 19 2016


MATHEMATICA

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; Select[Range[6000], binPalQ[#] && AllTrue[FactorInteger[#][[;; , 1]], binPalQ] &] (* Amiram Eldar, Mar 30 2021 *)


CROSSREFS

Cf. A006995, A163411, A207039.
Sequence in context: A329358 A180204 A006995 * A329419 A235264 A064896
Adjacent sequences: A163407 A163408 A163409 * A163411 A163412 A163413


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Jul 27 2009


EXTENSIONS

More terms from Sean A. Irvine, Nov 10 2009


STATUS

approved



