A173951 Positive integers with the property that if the base-3 representation is reversed the result is twice the original number.

32, 104, 320, 968, 2624, 2912, 7808, 8744, 23360, 25376, 26240, 70016, 75920, 78728, 209984, 212576, 227552, 233600, 236192, 629888, 638312, 682448, 700160, 708584, 1889600, 1897376, 1915520, 2047136, 2054912, 2099840, 2117984, 2125760

Offset

1,1

Comments

The number of terms of this sequence containing n ternary digits is given by {d(n)}={0,0,0,1,1,1,1,2,2,3,3,5,5,8,8,13,13,21,...} for n=1,2,3,... and thus appears to be essentially the doubling-up of the Fibonacci numbers A103609. For example, 2624 = 10121012(base-3) and 2912 = 10222212(base-3) are the only two terms that have 8 digits when written in base 3, so d(8)=2.

(This conjecture is correct - see A223077. - N. J. A. Sloane, Mar 19 2013)

All terms of sequence A173952, defined by b(1)=32 and, for n>1, b(n)=9*b(n-1)+32, appear to be terms of the above sequence {a(n)}; in fact each term b(n) appears to be the largest term of {a(k)} that has 2n+2 digits when written in base 3.

Links

Table of n, a(n) for n=1..32.

Crossrefs

Cf. A103609, A173952, A223077, A214927.

Sequence in context: A134845 A167982 A063498 * A233691 A337786 A233684

Adjacent sequences: A173948 A173949 A173950 * A173952 A173953 A173954

Keyword

nonn,base

Author

John W. Layman, Mar 03 2010

Status

approved