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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. 2
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

CROSSREFS

Cf. A006995, A163411, A207039.

Sequence in context: A305409 A180204 A006995 * A235264 A064896 A076188

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 February 17 03:56 EST 2019. Contains 320201 sequences. (Running on oeis4.)