Multiplicative order
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Two constants that do not walk at random
Pollard's factoring method trusts x² + c modulo a prime to repeat as soon as a random function would, after about √p steps. For c = 1 and c = 3 it does. For c = 0 and c = −2 it runs twelve to eighteen times longer on average, with almost no tail and enormous cycles, because those two maps are multiplication in disguise and their cycles are set by the order of 2 rather than by chance. Every other constant walks at random — including in the one respect in which x² + c is plainly not random, that it is two-to-one.
Fair in base two and not in base six
Almost every number has digits that look like fair coin tosses in every base, and almost no number anyone can name is known to. Stoneham's number, 1/(3·2³) + 1/(9·2⁹) + 1/(27·2²⁷) + …, is one of the few: its binary digits are provably fair. Written in base 6 the same number has a run of 121 zeros starting at the 730th digit, and a longer one at every power of three after — because in base 6 each of its terms is a terminating fraction, and the gaps between them never fill.
Named alongside it
The objects these essays reach for when they reach for this one.
Birthday problemChebyshev polynomialCollisionDecimal expansionDoubling mapEquidistributionNormal numberPollard rhoPrimitive rootRandom mappingShift mapSymbolic dynamics