A363965 Binary palindromic numbers whose digit sum and aliquot sum are also binary palindromic.

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

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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.

Cf. A001065, A007088, A007953.

Sequence in context: A261511 A146972 A102742 * A089044 A117646 A064857

Adjacent sequences: A363962 A363963 A363964 * A363966 A363967 A363968

Keyword

nonn,base

Author

Aakash Gautam, Jul 12 2023

Extensions

a(6) and beyond from Michael S. Branicky, Jul 24 2023

Status

approved