Sequences of Three Consecutive Strictly Increasing Euler Phi Values

Theorem

The following sequences of $3$ consecutive positive integers have the property that their Euler $\phi$ values are strictly increasing:

$\tuple {105, 106, 107}, \tuple {165, 166, 167}, \tuple {315, 316, 317}, \tuple {525, 526, 527}, \dots$

This article is complete as far as it goes, but it could do with expansion. In particular: Related sequences: A161962 (superset), A161963 You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Proof

\(\ds \map \phi {525}\)

\(=\)

\(\ds 240\)

$\phi$ of $525$

\(\ds \map \phi {526}\)

\(=\)

\(\ds 262\)

$\phi$ of $526$

\(\ds \map \phi {527}\)

\(=\)

\(\ds 480\)

$\phi$ of $527$

This needs considerable tedious hard slog to complete it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Finish}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $523$