|
Search: id:A161955
|
|
|
| A161955 |
|
TITO2(n): The operation A161594 in binary, digit-reversals carried out in base 2. |
|
+0
3
|
|
| 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 19, 13, 27, 7, 29, 15, 31, 1, 57, 17, 49, 9, 37, 19, 33, 5, 41, 21, 43, 11, 45, 23, 47, 3, 35, 19, 51, 13, 53, 27, 65, 7, 105, 29, 59, 15, 61, 31, 63, 1, 59, 57, 67, 17, 117, 49, 71, 9, 73, 37, 105, 19, 109
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
The TITO function in binary: Represent n as a product of its prime factors in binary.
Revert the binary digits of each of these factors, then multiply them with
the same multiplicities as in n--so the base-2 representation does not effect
the exponents in the canonical prime factorization. Reverse the product in binary to get a(n).
|
|
LINKS
|
T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova (tanyakh(AT)yahoo.com), Jul 07 2009]
|
|
FORMULA
|
a(n) = A030101(A162742(n)) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 2009
|
|
EXAMPLE
|
To calculate TITO2(n=99): 99 = 3^3*11. Prime factors 3 and 11 in binary are 11 and
1011 correspondingly. Reversing those numbers we get 11 and 1101. The product with
multiplicities is the binary product of 11*11*1101 = 1110101. Reversing that we
get 1010111, which corresponds to 87. Hence a(99) = 87.
|
|
MATHEMATICA
|
reverseBinPower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n, 2]], 2]^k fBin[n_] := FromDigits[ Reverse[IntegerDigits[ Times @@ Map[reverseBinPower, FactorInteger[n]], 2]], 2] Table[fBin[n], {n, 200}]
|
|
CROSSREFS
|
Cf. A161594
Sequence in context: A145799 A098985 A072963 this_sequence A000265 A106617 A040026
Adjacent sequences: A161952 A161953 A161954 this_sequence A161956 A161957 A161958
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 22 2009
|
|
EXTENSIONS
|
Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 03 2009
|
|
|
Search completed in 0.002 seconds
|
