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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

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

Crossrefs

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

Formula

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