A256179 Sequence of power towers in ascending order, using all possible permutations of 2s and 3s.

2, 3, 4, 8, 9, 16, 27, 81, 256, 512, 6561, 19683, 65536, 43046721, 134217728, 7625597484987, 2417851639229258349412352, 443426488243037769948249630619149892803, 115792089237316195423570985008687907853269984665640564039457584007913129639936

Offset

1,1

Comments

a(n) is found by treating the digits of A248907(n) as power towers, so the sequence starts 2, 3, 2^2=4, 2^3=8, 3^2=9, 2^(2^2)=16, 3^3=27, 3^(2^2)=81, 2^(2^3)=256...

Links

Table of n, a(n) for n=1..19.

Vladimir Reshetnikov, 2-3 sequence puzzle, SeqFan list, Mar 18 2015.

Formula

A256179 = A256229 o A248907 = A256229 o A032810 o A185969, i.e., a(n) = A256229(A248907(n)) = A256229(A032810(A185969(n))).

Recurrence: a(1)=2, a(2)=3, a(3)=2^2, a(4)=2^3, a(5)=3^2, a(6)=2^(2^2), a(7)=3^3, a(8)=3^(2^2), a(9)=2^(2^3), a(10)=2^(3^2), a(11)=3^(2^3), a(12)=3^(3^2); and for n>6, a(2n)=3^a(n-1), a(2n-1)=2^a(n-1). - Vladimir Reshetnikov, Mar 19 2015

Example

a(12) = 19683 because A248907(12) = 332, and 3^(3^2) = 19683.

Prog

(PARI) A256179(n)=A256229(A248907[n])) \\ where A248907 is assumed to be defined as vector. - M. F. Hasler, Mar 19 2015

Crossrefs

Cf. A185969, A248907, A075877.

Sequence in context: A074311 A076382 A006899 * A078830 A304521 A026489

Adjacent sequences: A256176 A256177 A256178 * A256180 A256181 A256182

Keyword

nonn

Author

Bob Selcoe, Mar 18 2015

Extensions

More terms from M. F. Hasler, Mar 19 2015

Status

approved