Langford's Problem

Arrange copies of the digits 1, ..., such that there is one digit between the 1s, two digits between the 2s, etc. For example, the solution is 312132 and the solution is 41312432. Solutions exist only if . Thenumber of solutions for , 4, 5, ... are 1, 1, 0, 0, 26, 150, 0, 0, 17792, 108144, ... (Sloane's A014552).

References

Gardner, M. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 70 and 77-78, 1978.

Sloane, N. J. A. Sequence A014552in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Prime Pairs
• Prime Patterns Conjecture
• Prime Polynomial
• Prime Power Conjecture
• Prime Power Symbol
• Primequad
• Prime Quadratic Effect
• Prime Quadruplet
• Prime Representation
• Prime Ring
• Prime Sequence
• Prime Spiral
• Prime String
• Prime Sum
• Prime Theta Function
• Prime Triangle
• Prime Unit
• Prime Zeta Function
• Primitive Abundant Number
• Primitive Function
• Primitive Irreducible Polynomial
• Primitive Polynomial Modulo 2
• Primitive Prime Factor
• Primitive Pseudoperfect Number
• Primitive Recursive Function