login
A334530
Numbers that are both binary palindromes and binary Smith numbers.
3
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 05 2020
STATUS
approved