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Saturday, July 30, 2011

Pluperfect Digital Invariants

A Pluperfect Digital Invariants or PPDI aka Armstrong Number is a number which is equal to the sum of a power of its digits.

For example:

$153 = 1^3 + 5^3 + 3^3$.
$1634 = 1^4 + 6^4 + 3^4 + 4^4$.
$54748 = 5^5 + 4^5 + 7^5 + 4^5 + 8^5$

The largest ( known? ) PPDI is $$115 132 219 018 763 992 565 095 597 973 971 522 401$$ which is equal to the sum of the 39th power of its digits.

These facts belong to the realm of mathematics, of course. But we get rather close to what I call anti-mathematics: numerology.

As soon as you discard scientific rigor, you're no longer a mathematician, you're a numerologist.

Sol Robeson in Pi

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