Digital Root
Consider the process of taking a number, adding its Digits, then adding the Digits ofnumbers derived from it, etc., until the remaining number has only one Digit. The number of additions required toobtain a single Digit from a number 
is called the Additive Persistence of , and the Digitobtained is called the digital root of .
For example, the sequence obtained from the starting number 9876 is (9876, 30, 3), so 9876 has an AdditivePersistence of 2 and a digital root of 3. The digital roots of the first few integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1,2, 3, 4, 5, 6, 7, 9, 1, ... (Sloane's A010888). The digital root of an Integer can therefore be computedwithout actually performing the iteration using the simple congruence formula
See also Additive Persistence, Digitaddition, Kaprekar Number,Multiplicative Digital Root, Multiplicative Persistence, Narcissistic Number,Recurring Digital Invariant, Self Number
References
Sloane, N. J. A. SequencesA010888 andA007612/M1114in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Lagrange Polynomial
- Lagrange Remainder
- Lagrange Resolvent
- Lagrange's Continued Fraction Theorem
- Lagrange's Equation
- Lagrange's Four-Square Theorem
- Lagrange's Group Theorem
- Lagrange's Identity
- Lagrange's Interpolating Fundamental Polynomial
- Lagrange's Lemma
- Lagrange Spectrum
- Lagrangian Coefficient
- Lagrangian Derivative
- Laguerre Differential Equation
- Laguerre-Gauss Quadrature
- Laguerre Polynomial
- Laguerre Quadrature
- Laguerre's Method
- Laguerre's Repeated Fraction
- Laisant's Recurrence Formula
- Lakshmi Star
- Lal's Constant
- Laman's Theorem
- Lambda Calculus
- Lambda Function