A243407 Decimal expansion of Pálfy's constant c_3 = 5/3 + log_9(32).

3, 2, 4, 3, 9, 9, 1, 0, 5, 0, 5, 9, 5, 3, 1, 0, 2, 5, 9, 4, 1, 5, 4, 8, 4, 4, 5, 2, 5, 2, 3, 5, 6, 8, 8, 0, 2, 4, 1, 5, 6, 3, 0, 7, 6, 6, 9, 9, 6, 3, 6, 7, 7, 3, 6, 3, 4, 3, 3, 0, 4, 0, 2, 6, 2, 6, 3, 3, 7, 9, 6, 7, 0, 1, 1, 8, 9, 5, 3, 6, 7, 9, 3, 1, 9

Offset: 1

Author

Charles R Greathouse IV, Jun 04 2014

Keywords

• nonn
• cons
• nice

Comments

Pálfy proved there are no primitive solvable permutation groups T with order greater than n^c_3 / 24^(1/3) but infinitely many for which equality is attained, where n is the degree of the group. Such groups necessarily have degree which is a power of 3, hence the subscript. He also gave tighter bounds for other prime powers.

Examples

			E(9) : 2S_4 is a primitive solvable permutation group of degree 9 and order 432 = 9^(5/3 + log_9(32))/24^(1/3).
		

Links

• P. P. Pálfy, A polynomial bound for the orders of primitive solvable groups, J. Algebra 77:1 (1982), pp. 127-137.
• Index entries for transcendental numbers

Crossrefs

Cf. A000019.

Programs

Mathematica

RealDigits[5/3+Log[9,32],10,120][[1]] (* Harvey P. Dale, Mar 05 2015 *)

PARI

5/3+log(32)/log(9)