cp's OEIS Frontend

A248907 Numbers consisting only of digits 2 and 3, ordered according to the value obtained when the digits are interspersed with (right-associative) ^ operators.

%I A248907 #50 Dec 23 2024 14:53:44
%S A248907 2,3,22,23,32,222,33,322,223,232,323,332,2222,3222,233,333,2322,3322,
%T A248907 2223,3223,2232,3232,2323,3323,2332,3332,22222,32222,23222,33222,2233,
%U A248907 3233,2333,3333,22322,32322,23322,33322,22223,32223,23223,33223,22232,32232
%N A248907 Numbers consisting only of digits 2 and 3, ordered according to the value obtained when the digits are interspersed with (right-associative) ^ operators.
%C A248907 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
%C A248907 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
%H A248907 Vladimir Reshetnikov, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-March/014595.html">2-3 sequence puzzle</a>, SeqFan list, Mar 18 2015.
%H A248907 Vladimir Reshetnikov et al., <a href="http://math.stackexchange.com/questions/1196327/power-towers-of-2-and-3-looking-for-a-proof">Power towers of 2 and 3 - looking for a proof</a>, on StackExchange.com, Mar 19 2015
%F A248907 a(n) = A032810(A185969(n)).
%t A248907 ClearAll[a, p];
%t A248907 p[d_, n_] := d 10^IntegerLength[n] + n;
%t A248907 a[n_ /; n <= 12] := a[n] = {2, 3, 22, 23, 32, 222, 33, 322, 223, 232, 323, 332}[[n]];
%t A248907 a[n_ /; OddQ[n]]  := a[n] = p[2, a[(n - 1)/2]];
%t A248907 a[n_] := a[n] = p[3, a[(n - 2)/2]];
%t A248907 Array[a, 100]
%o A248907 (Haskell)
%o A248907 a248907 = a032810 . a185969
%o A248907 (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
%Y A248907 Cf. A032810, A185969, A256179, A256229.
%Y A248907 For another version, see A299229 (each digit is a separate term).
%K A248907 nonn,easy
%O A248907 1,1
%A A248907 _Vladimir Reshetnikov_ and _Reinhard Zumkeller_, Mar 18 2015
%E A248907 Edited by _M. F. Hasler_, Mar 21 2015