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The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. A059756: Sierpinski numbers: 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ... Odd k for which { k⋅2 n + 1 : n ∈ } consists only of composite numbers. A076336
Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
105 is the 14th triangular number, [1] a dodecagonal number, [2] and the first Zeisel number. [3] It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7. [4] It is also the sum of the first five square pyramidal numbers. 105 comes in the middle of the prime quadruplet (101, 103 ...
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7.
The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2] [3] The idea of the look-and-say sequence is similar to that of run-length encoding. If started with any digit d from 0 to 9 then d will remain indefinitely as the last digit of the sequence.
Let [a, b, c] be a primitive triple with a odd. Then 3 new triples [a 1, b 1, c 1], [a 2, b 2, c 2], [a 3, b 3, c 3] may be produced from [a, b, c] using matrix multiplication and Berggren's [11] three matrices A, B, C. Triple [a, b, c] is termed the parent of the three new triples (the children). Each child is itself the parent of 3 more ...
The addition, subtraction and multiplication of even and odd integers obey simple rules. The addition or subtraction of two even numbers or of two odd numbers always produces an even number, e.g., 4 + 6 = 10 and 3 + 5 = 8. Conversely, the addition or subtraction of an odd and even number is always odd, e.g., 3 + 8 = 11. The multiplication of ...