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 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 (list; graph; refs; listen; history; text; internal format)
 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^(Ln-i), 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/2-1)..2^(d/2)-1)}   else     m:= (d-1)/2;     B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};     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, 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

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)