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%I #14 Sep 26 2023 17:49:15
%S 1,3,5,7,45,313,403,1501,1619,2193,2661,5349,11997,21477,21653,24029,
%T 27499,81017,98563,104147,116423,251823,269761,284881,288049,320057,
%U 337189,344037,368077,400067,410899,413779,428683,440171,475159,523007,678309,823059
%N Binary palindromic numbers whose digit sum and aliquot sum are also binary palindromic.
%H Michael S. Branicky, <a href="/A363965/b363965.txt">Table of n, a(n) for n = 1..10000</a>
%e 45 is a term since 45 = 101101_2, A007953(45) = 4+5 = 9 = 1001_2, A001065(45) = 33 = 100001_2, and all of those binary expansions are palindromes.
%t binPalQ[n_] := PalindromeQ[IntegerDigits[n, 2]]; Select[Range[10^6], AllTrue[{#, Plus @@ IntegerDigits[#], DivisorSigma[1, #] - #}, binPalQ] &] (* _Amiram Eldar_, Jul 28 2023 *)
%o (Python)
%o from sympy import divisor_sigma as s1
%o def bp(n): return (b:=bin(n)[2:])==b[::-1]
%o def ok(n): return n and bp(n) and bp(sum(map(int,str(n)))) and bp(s1(n)-n)
%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Jul 24 2023
%Y Subsequence of A006995.
%Y Cf. A001065, A007088, A007953.
%K nonn,base
%O 1,2
%A _Aakash Gautam_, Jul 12 2023
%E a(6) and beyond from _Michael S. Branicky_, Jul 24 2023