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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 05 2020
STATUS
approved

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Last modified February 20 17:05 EST 2024. Contains 370213 sequences. (Running on oeis4.)