196 (number)

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← 195 196 197 →
Cardinal one hundred ninety-six
Ordinal 196th
(one hundred ninety-sixth)
Factorization 22 × 72
Divisors 1, 2, 4, 7, 14, 28, 49, 98, 196
Greek numeral ΡϞϚ´
Roman numeral CXCVI
Binary 110001002
Ternary 210213
Senary 5246
Octal 3048
Duodecimal 14412
Hexadecimal C416

196 (one hundred [and] ninety-six) is the natural number following 195 and preceding 197.

Contents

In mathematics

196 is a square number, the square of 14. As the square of a Catalan number, it counts the number of walks of length 8 in the positive quadrant of the integer grid that start and end at the origin, moving diagonally at each step. [1] It is part of a sequence of square numbers beginning 0, 1, 4, 25, 196, ... in which each number is the smallest square that differs from the previous number by a triangular number. [2]

There are 196 one-sided heptominoes, the polyominoes made from 7 squares. Here, one-sided means that asymmetric polyominoes are considered to be distinct from their mirror images. [3]

A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its digits and adding the resulting numbers. 196 is the smallest number conjectured to be a Lychrel number in base 10; the process has been carried out for over a billion iterations without finding a palindrome, but no one has ever proven that it will never produce one. [4] [5]

See also

Related Research Articles

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA001246(Squares of Catalan numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA036449(Values square, differences triangular)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA000988(Number of one-sided polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA023108(A023108)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Gabai, Hyman; Coogan, Daniel (1969). "On palindromes and palindromic primes". Mathematics Magazine. 42 (5): 252–254. doi:10.2307/2688705. JSTOR   2688705. MR   0253979.
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