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A363965
Binary palindromic numbers whose digit sum and aliquot sum are also binary palindromic.
1
1, 3, 5, 7, 45, 313, 403, 1501, 1619, 2193, 2661, 5349, 11997, 21477, 21653, 24029, 27499, 81017, 98563, 104147, 116423, 251823, 269761, 284881, 288049, 320057, 337189, 344037, 368077, 400067, 410899, 413779, 428683, 440171, 475159, 523007, 678309, 823059
OFFSET
1,2
LINKS
EXAMPLE
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.
MATHEMATICA
binPalQ[n_] := PalindromeQ[IntegerDigits[n, 2]]; Select[Range[10^6], AllTrue[{#, Plus @@ IntegerDigits[#], DivisorSigma[1, #] - #}, binPalQ] &] (* Amiram Eldar, Jul 28 2023 *)
PROG
(Python)
from sympy import divisor_sigma as s1
def bp(n): return (b:=bin(n)[2:])==b[::-1]
def ok(n): return n and bp(n) and bp(sum(map(int, str(n)))) and bp(s1(n)-n)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 24 2023
CROSSREFS
Subsequence of A006995.
Sequence in context: A261511 A146972 A102742 * A089044 A117646 A064857
KEYWORD
nonn,base
AUTHOR
Aakash Gautam, Jul 12 2023
EXTENSIONS
a(6) and beyond from Michael S. Branicky, Jul 24 2023
STATUS
approved