In this document, the range of appearance I(r) of a positive integer r in heptagonal numbers and some results by comparing I(r) with Legendre symbol, p- adic range and prime conjunction function of r are accessible. Since I(r) does not possess a meticulous prototype, all the results are confirmed by Java program for all-natural numbers r?N.
In this paper, the range of appearance I(r) of a positive integer r in heptagonal numbers is defined and limited number of results consisting I(r), legendre symbol, p- adic range and prime conjunction function of r are evaluated. Entire results are inveterate by Java program for all positive values of r. In this approach, one can define the range of appearance of an integer in other polygonal numbers and may analyse their results by comparing the values of I(r) with Jacobi symbol, quadratic residue and non-residue modulo r.
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