What is a Heptagon Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles.

If a number conforms to a special rule, I call it a Heptagon Number™.
Use the following examples below to find the rule.

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} \def\Title{\textbf{ Heptagon }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Numbers}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 12 }&\text{ 14 }\\ \hline \text{ 31 }&\text{ 33 }\\ \hline \text{ 47 }&\text{ 49 }\\ \hline \text{ 88 }&\text{ 90 }\\ \hline \text{ 234 }&\text{ 236 }\\ \hline \text{ 597 }&\text{ 599 }\\ \hline \text{ 815 }&\text{ 817 }\\ \hline \text{ 901 }&\text{ 903 }\\ \hline \text{ 1,689 }&\text{ 1,691 }\\ \hline \text{ 6,667 }&\text{ 6,669 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Heptagon Numbers™,Not Heptagon Numbers™
12,14
31,33
47,49
88,90
234,236
597,599
815,817
901,903
1689,1691
6667,6669


A Heptagon number is

A number that when shown on a 7-segment display uses a multiple of 7 segments, thus the prefix hepta-.

For each listed number:

12 -> 2 + 5 = 7
31 -> 5 + 2 = 7
47 -> 4 + 3 = 7
88 -> 7 + 7 = 14
234 -> 5 + 5 + 4 = 14
597 -> 5 + 6 + 3 = 14
815 -> 7 + 2 + 5 = 14
901 -> 6 + 6 + 2 = 14
1689 -> 2 + 6 + 7 + 6 = 21
6667 -> 6 + 6 + 6 + 3 = 21

The numbers in the other column do not have this property.

• You got it. Nice Work~! Sep 19, 2019 at 1:28