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"subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence.
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. [1] This set of preferred numbers was proposed ca. 1877 by French army engineer Colonel Charles Renard [ 2 ] [ 3 ] [ 4 ] and reportedly published in an 1886 instruction for captive balloon troops, thus receiving the current name in ...
If a pair of numbers modulo n appears twice in the sequence, then there's a cycle. If we assume the main statement is false, using the previous statement, then it would imply there's infinite distinct pairs of numbers between 0 and n-1, which is false since there are n 2 such pairs.
The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. [3] The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, ... .
ISO 7010 is an International Organization for Standardization technical standard for graphical hazard symbols on hazard and safety signs, including those indicating emergency exits. It uses colours and principles set out in ISO 3864 for these symbols, and is intended to provide "safety information that relies as little as possible on the use of ...
It might be 11:11 or 3:33. Maybe repeating numbers have made their way into other aspects of your life, such as a receipt that totaled $22.22 . These may seem like mere coincidences, but for some ...
The first few terms of the sequence are 1, 1, 3, 7, 17, 41, 99, … (sequence A001333 in the OEIS). Each term in this sequence is half the corresponding term in the sequence of companion Pell numbers. These numbers also appear in the continued fraction convergents to √ 2.
Only F sequences with (i,j) = (0,0), (0,1), (1,0), and (1,1), the first of which represents the original Q sequence, appear to be well-defined. [21] Unlike Q (1), the first elements of the Pinn F i , j ( n ) sequences are terms of summations in calculating later elements of the sequences when any of the additional constants is 1.