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In mathematics, and in particular in arithmetic combinatorics, a Salem-Spencer set is a set of numbers no three of which form an arithmetic progression. Salem–Spencer sets are also called 3-AP-free sequences or progression-free sets. They have also been called non-averaging sets, [ 1][ 2] but this term has also been used to denote a set of ...
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Field 3 begins with a '+' character and is optionally followed by the same sequence identifier (and any description) again. Field 4 encodes the quality values for the sequence in Field 2, and must contain the same number of symbols as letters in the sequence. A FASTQ file containing a single sequence might look like this:
In number theory, Sylvester's sequence is an integer sequence in which each term is the product of the previous terms, plus one. Its first few terms are. 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence A000058 in the OEIS ). Sylvester's sequence is named after James Joseph Sylvester, who first investigated it ...
For example, the sequence,,,,, … is not an arithmetic progression, but is instead generated by starting with 17 and adding either 3 or 5, thus allowing multiple common differences to generate it. A semilinear set generalizes this idea to multiple dimensions -- it is a set of vectors of integers, rather than a set of integers.
In molecular biology, a reading frame is a way of dividing the sequence of nucleotides in a nucleic acid ( DNA or RNA) molecule into a set of consecutive, non-overlapping triplets. Where these triplets equate to amino acids or stop signals during translation, they are called codons . A single strand of a nucleic acid molecule has a phosphoryl ...
Arithmetic progression. An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13 ...
e. In mathematics, arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. Put plainly, the n th term of an arithmetico-geometric sequence is the product of the n th term of an arithmetic sequence and the n th term of a geometric one. [ 1]
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