A334530 Numbers that are both binary palindromes and binary Smith numbers.

15, 51, 85, 471, 765, 771, 843, 951, 1023, 1285, 1501, 1707, 2015, 3687, 3831, 4095, 4369, 4777, 5621, 5917, 6077, 6483, 6643, 6891, 6939, 7003, 7099, 7447, 7671, 10041, 11565, 12093, 13011, 14631, 15063, 15855, 20345, 20473, 22517, 23213, 26067, 26483, 26611

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

15 is a term since its binary representation, 1111, is palindromic, and its prime factorization, 3 * 5, is 11 * 101 in binary representation, and 1 + 1 + 1 + 1 = (1 + 1) + (1 + 0 + 1).

Mathematica

binPalSmithQ[n_] := PalindromeQ[(d = IntegerDigits[n, 2])] && CompositeQ[n] && Plus @@ (Last@# * DigitCount[First@#, 2, 1] & /@ FactorInteger[n]) == Plus @@ d; Select[Range[10^5], binPalSmithQ]

Crossrefs

Intersection of A006995 and A278909.

Cf. A098834.

Sequence in context: A075933 A075929 A337295 * A044117 A044498 A138082

Adjacent sequences: A334527 A334528 A334529 * A334531 A334532 A334533

Keyword

nonn,base

Author

Amiram Eldar, May 05 2020

Status

approved