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Consecutive primes in arithmetic progression refers to at least three consecutive primes which are consecutive terms in an arithmetic progression. Note that unlike an AP-k, all the other numbers between the terms of the progression must be composite. For example, the AP-3 {3, 7, 11} does not qualify, because 5 is also a prime.
A scientific law is "inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present". [7] The production of a summary description of our environment in the form of such laws is a fundamental aim of science.
Subsequences can contain consecutive elements which were not consecutive in the original sequence. A subsequence which consists of a consecutive run of elements from the original sequence, such as ,, , from ,,,,, , is a substring. The substring is a refinement of the subsequence.
In the graph the sequence appears to be converging to a limit as the distance between consecutive terms in the sequence gets smaller as n increases. In the real numbers every Cauchy sequence converges to some limit. A Cauchy sequence is a sequence whose terms become arbitrarily close together as n gets very large.
Dr. Dinesh Prasad Saklani is the director of NCERT since 2022. [2] In 2023, NCERT constituted a 19-member committee, including author and Infosys Foundation chair Sudha Murthy, singer Shankar Mahadevan, and Manjul Bhargava to finalize the curriculum, textbooks and learning material for classes 3 to 12. [4]
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
The amendment was a response to the four-term presidency of Franklin D. Roosevelt, which amplified longstanding debates over term limits.. The Twenty-second Amendment was a reaction to Franklin D. Roosevelt's election to an unprecedented four terms as president, but presidential term limits had long been debated in American politics.
As a second example, for sequences in the real numbers, weak positivity (is for all ?) reduces to positivity of the sequence (because the answer must be negated, this is a Turing reduction). The Skolem-Mahler-Lech theorem would provide answers to some of these questions, except that its proof is non-constructive .