This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334532 #10 May 06 2020 01:46:32 %S A334532 22517,317273,5876429,7129499,18659953,20053785,24328605,28676955, %T A334532 31134135,88700053,92254197,95682157,96316909,97462173,117812487, %U A334532 120026919,120303271,120323751,128167471,133396095,133984767,292610513,309416393,314572713,348580965,351400421 %N A334532 Binary palindromic numbers that are also binary Niven and binary Smith numbers. %H A334532 Amiram Eldar, <a href="/A334532/b334532.txt">Table of n, a(n) for n = 1..779</a> %H A334532 Amin Witno, <a href="https://www.emis.de/journals/INTEGERS/papers/o66/o66.Abstract.html">Smith Numbers With Extra Digital Features</a>, Integers, Vol. 14 (2014), Article A66. %e A334532 The binary representation of 22517 is 101011111110101 which is palindromic. The number of 1's in its binary representation is 11 which is a divisor of 22517, hence 22517 is a binary Niven. It is also a binary Smith number since its prime factorization, 11 * 23 * 89, is 1011 * 10111 * 1011001 in binary representation, and (1 + 0 + 1 + 1) + (1 + 0 + 1 + 1 + 1) + (1 + 0 + 1 + 1 + 0 + 0 + 1) = 3 + 4 + 4 = 11 is equal to the number of 1's in its binary representation. %t A334532 binWt[n_] := DigitCount[n, 2, 1]; binPalNivenSmithQ[n_] := Divisible[n, (bw = Plus @@ (d = IntegerDigits[n, 2]))] && PalindromeQ[d] && CompositeQ[n] && Plus @@ (Last@# * binWt[First@#] & /@ FactorInteger[n]) == bw; Select[Range[2*10^6], binPalNivenSmithQ] %Y A334532 Intersection of A006995, A049445 and A278909. %Y A334532 Intersection of any two of the sequences A334529, A334530 and A334531. %Y A334532 Cf. A334528. %K A334532 nonn,base %O A334532 1,1 %A A334532 _Amiram Eldar_, May 05 2020