

A334532


Binary palindromic numbers that are also binary Niven and binary Smith numbers.


1



22517, 317273, 5876429, 7129499, 18659953, 20053785, 24328605, 28676955, 31134135, 88700053, 92254197, 95682157, 96316909, 97462173, 117812487, 120026919, 120303271, 120323751, 128167471, 133396095, 133984767, 292610513, 309416393, 314572713, 348580965, 351400421
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OFFSET

1,1


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..779
Amin Witno, Smith Numbers With Extra Digital Features, Integers, Vol. 14 (2014), Article A66.


EXAMPLE

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.


MATHEMATICA

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]


CROSSREFS

Intersection of A006995, A049445 and A278909.
Intersection of any two of the sequences A334529, A334530 and A334531.
Cf. A334528.
Sequence in context: A235415 A235260 A236085 * A249614 A153770 A235067
Adjacent sequences: A334529 A334530 A334531 * A334533 A334534 A334535


KEYWORD

nonn,base


AUTHOR

Amiram Eldar, May 05 2020


STATUS

approved



