A334532 Binary palindromic numbers that are also binary Niven and binary Smith numbers.

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

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