“Palindromic Number Conjecture”的概念、定义、习题解题方法及翻译-数学辞典

单词

Palindromic Number Conjecture

释义

Palindromic Number Conjecture

Apply the 196-Algorithm, which consists of taking any Positive Integer of two digits or more, reversing thedigits, and adding to the original number. Now sum the two and repeat the procedure with the sum. Of the first 10,000 numbers,only 251 do not produce a Palindromic Number in steps (Gardner 1979).

It was therefore conjectured that all numbers will eventually yield a Palindromic Number. However, the conjecturehas been proven false for bases which are a Power of 2, and seems to be false for base 10 as well. Among the first100,000 numbers, 5,996 numbers apparently never generate a Palindromic Number (Gruenberger 1984). The first few are196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, ... (Sloane's A006960).

It is conjectured, but not proven, that there are an infinite number of palindromic Primes. With the exceptionof 11, palindromic Primes must have an Odd number of digits.

See also 196-Algorithm

References

Gardner, M. Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American. New York: Knopf, pp. 242-245, 1979.

Gruenberger, F. ``How to Handle Numbers with Thousands of Digits, and Why One Might Want to.'' Sci. Amer. 250, 19-26, Apr. 1984.

Sloane, N. J. A. SequenceA006960/M5410in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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