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%I #8 May 06 2020 01:46:29
%S 15,51,85,471,765,771,843,951,1023,1285,1501,1707,2015,3687,3831,4095,
%T 4369,4777,5621,5917,6077,6483,6643,6891,6939,7003,7099,7447,7671,
%U 10041,11565,12093,13011,14631,15063,15855,20345,20473,22517,23213,26067,26483,26611
%N Numbers that are both binary palindromes and binary Smith numbers.
%H Amiram Eldar, <a href="/A334530/b334530.txt">Table of n, a(n) for n = 1..10000</a>
%e 15 is a term since its binary representation, 1111, is palindromic, and its prime factorization, 3 * 5, is 11 * 101 in binary representation, and 1 + 1 + 1 + 1 = (1 + 1) + (1 + 0 + 1).
%t binPalSmithQ[n_] := PalindromeQ[(d = IntegerDigits[n, 2])] && CompositeQ[n] && Plus @@ (Last@# * DigitCount[First@#, 2, 1] & /@ FactorInteger[n]) == Plus @@ d; Select[Range[10^5], binPalSmithQ]
%Y Intersection of A006995 and A278909.
%Y Cf. A098834.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, May 05 2020
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