Note that for any given series of numbers a1 .. ak there's a polynomial f(x) of degree less then or equal to k-1 such that f(1) == a1, f(2) == a2, etc. For obvious reasons, all the coefficients of f(x) are rational (otherwise, f(x) cannot be an integer for integer x).

Given that there's at least one function that uses only the given operations, and a finite number of such operations, there's also one that uses the smallest number of operators. But it's not necessarily unique.

I don't know whether this is helpful.

In reply to Re^3: Challenge: Simple algorithm for continuing series of integers by JavaFan
in thread Challenge: Simple algorithm for continuing series of integers by moritz

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.