Positive Integers Not Expressible as Sum of Distinct Non-Pythagorean Primes
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Theorem
The following positive integers cannot be expressed as the sum of distinct non-pythagorean primes:
- $1, 2, 4, 5, 6, 8, 9, 12, 13, 15, 16, 17, 20, 24, 25, 27, 28, 32, 35, 36, 39, 48, 51, 55$
This sequence is A048262 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
All positive integers greater than $55$ can be so expressed.
Proof
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Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $55$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $55$