A001144 An exponential function on partitions (next term is 2^512). (Formerly M0593 N0214)

1, 2, 3, 4, 9, 27, 512, 134217728

Offset

1,2

Comments

Largest number that can be expressed in the form a_1 ^ a_2 ^ ... ^ a_k, where a_1 + a_2 + ... + a_k = n. - Franklin T. Adams-Watters, Apr 09 2010

Equivalently, largest number that can be expressed using the constant 1 exactly n times with only addition and exponentiation -- no concatenation of digits is allowed. (Comment to facilitate searching.) - Rick L. Shepherd, Jun 14 2017

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..8.

S. W. Golomb and Judith Richman, Problem E2118, Amer. Math. Monthly, 76 (1969), 830-831.

Formula

For n >= 7, a(n) = 2^a(n-2). - Franklin T. Adams-Watters, Apr 09 2010

Crossrefs

Cf. A000792, A014221. - Franklin T. Adams-Watters, Apr 09 2010

Sequence in context: A076381 A282571 A063455 * A121253 A014118 A007704

Adjacent sequences: A001141 A001142 A001143 * A001145 A001146 A001147

Keyword

nonn

Author

N. J. A. Sloane

Status

approved