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A248907
Numbers consisting only of digits 2 and 3, ordered according to the value obtained when the digits are interspersed with (right-associative) ^ operators.
7
2, 3, 22, 23, 32, 222, 33, 322, 223, 232, 323, 332, 2222, 3222, 233, 333, 2322, 3322, 2223, 3223, 2232, 3232, 2323, 3323, 2332, 3332, 22222, 32222, 23222, 33222, 2233, 3233, 2333, 3333, 22322, 32322, 23322, 33322, 22223, 32223, 23223, 33223, 22232, 32232
OFFSET
1,1
COMMENTS
A256179(n) is found by treating the digits of a(n) as power towers. So for example, a(11) = 323, so A256179(11) = 6561 because 3^(2^3) = 6561. - Bob Selcoe, Mar 18 2015
This is a permutation of the list A032810 (numbers having only digits 2 and 3) in the sense that is a list with exactly the same terms but in different order, namely such that the ("power tower") function A256229 yields an increasing sequence. The permutation of the indices is given by A185969, cf. formula. - M. F. Hasler, Mar 21 2015
LINKS
Vladimir Reshetnikov, 2-3 sequence puzzle, SeqFan list, Mar 18 2015.
Vladimir Reshetnikov et al., Power towers of 2 and 3 - looking for a proof, on StackExchange.com, Mar 19 2015
FORMULA
a(n) = A032810(A185969(n)).
MATHEMATICA
ClearAll[a, p];
p[d_, n_] := d 10^IntegerLength[n] + n;
a[n_ /; n <= 12] := a[n] = {2, 3, 22, 23, 32, 222, 33, 322, 223, 232, 323, 332}[[n]];
a[n_ /; OddQ[n]] := a[n] = p[2, a[(n - 1)/2]];
a[n_] := a[n] = p[3, a[(n - 2)/2]];
Array[a, 100]
PROG
(Haskell)
a248907 = a032810 . a185969
(PARI) vecsort(A032810, (a, b)->A256229(a)>A256229(b)) \\ Assuming that A032810 is defined as a vector. Append [1..N] if the vector A032810 has too many (thus too large) elements: recall that 33333 => 3^(3^(3^(3^3))). - M. F. Hasler, Mar 21 2015
CROSSREFS
For another version, see A299229 (each digit is a separate term).
Sequence in context: A163902 A154865 A032810 * A062921 A298470 A083178
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Mar 21 2015
STATUS
approved