scholarly journals Iteration of the number-theoretic function f(2n) = n, f(2n + 1) = 3n + 2

1976 ◽  
Author(s):  
C Everett
Keyword(s):  
Theoretic Function

A Method of Tabulating the Number-Theoretic Function g(k)

1992 ◽  
Vol 59 (199) ◽  
pp. 251 ◽  
Author(s):  
Renate Scheidler ◽  
Hugh C. Williams
Keyword(s):  
Theoretic Function

scholarly journals The Series Σ∞1 f(n)/n for Periodic f

1965 ◽  
Vol 8 (4) ◽  
pp. 413-432 ◽  
Author(s):  
Arthur E. Livingston
Keyword(s):  
Positive Integer ◽  
Complex Valued ◽  
Theoretic Function

We are here concerned with the problem of deciding when Σ∞n=1 f(n)/n ≠ 0, given that f is periodic and the series convergent. In particular, we considerConjecture A. Let p be a positive integer and f a (real-or complex-valued) number-theoretic function with period p.

scholarly journals Iterates of a number-theoretic function

1969 ◽  
Vol 23 (105) ◽  
pp. 181-181 ◽  
Author(s):  
Mohan Lal
Keyword(s):  
Theoretic Function

scholarly journals A method of tabulating the number-theoretic function $g(k)$

1992 ◽  
Vol 59 (199) ◽  
pp. 251-251
Author(s):  
Renate Scheidler ◽  
Hugh C. Williams
Keyword(s):  
Theoretic Function

Can there be no nonrecursive functions?

1971 ◽  
Vol 36 (2) ◽  
pp. 309-315 ◽  
Author(s):  
Joan Rand Moschovakis
Keyword(s):  
Free Choice ◽  
Church’S Thesis ◽  
Recursive Functions ◽  
Choice Sequence ◽  
Church's Thesis ◽  
Theoretic Function ◽  
Ordinary Number ◽  
Definable Function

In 1936 Alonzo Church proposed the following thesis: Every effectively computable number-theoretic function is general recursive. The classical mathematician can easily give examples of nonrecursive functions, e.g. by diagonalizing a list of all general recursive functions. But since no such function has been found which is effectively computable, there is as yet no classical evidence against Church's Thesis.The intuitionistic mathematician, following Brouwer, recognizes at least two notions of function: the free-choice sequence (or ordinary number-theoretic function, thought of as the ever-finite but ever-extendable sequence of its values) and the sharp arrow (or effectively definable function, all of whose values can be specified in advance).

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