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References to 'descending order'
1. $px + 1$ map by PrimeFan
2. Collatz sequences starting with numbers of the form $3n + 1$ for odd $n < 334$ by PrimeFan
3. examples of aliquot sequences by PrimeFan
4. examples supporting the Erd\H{o}s-Straus conjecture by PrimeFan
5. Hultsch-Bruins method by milogardner
6. Kaprekar constant by PrimeFan
7. power of two by 1and2and4
8. proof that the sum of the iterated totient function is always odd by PrimeFan
9. singular value decomposition by akrowne
10. Zeckendorf's theorem by CompositeFan