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183:σ(A+B)=σ(A)+σ(B); σ(A×B)=σ(A)×σ(B); σ(A)=, σ(2)=1,2,4,8,7,5 for j=0,1,2,3,4,5, respectively. σ(3)=1,3,9 for k=0,1 and k not smaller than 2, respectively. σ(4)=1,4,7 for j=0,1,2, respectively. σ(5)=1,5,7,8,4,2 for j=0,1,2,3,4,5, respectively. σ(6)=1,6,9 for k=0,1 and k not smaller than 2, respectively. σ(7)=1,7,4 for j=0,1,2, respectively. σ(8)=1,8 for j=0,1, respectively.
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The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit.
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Would be nice if someone could add a more generalised rule to the mod 9 for base 10. I'm sure it would just be mod (base-1) but the answer could be more tricky to interpret. For example, in binary ds(101) = 10?
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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The digit sum and digital root aren't the same, as you can read in the
Applications section of the article:
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I added info by a doctor in metaphysical philosophy upon advice from another user on the numerology page.
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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Suppose we want to find σ(314159265358979). Let us state some basic operations and some periodicities:
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on
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before doing mass systematic removals. This message is updated dynamically through the template
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Let σ(M) be the digit sum of positive integer M. We all know from casting nines that σ(9k+r)=r.
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It seems to me if S(n) is a digit sum of n (in any base), then for any a,b:
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For the example, 314159265358979=9m+5, and 2718281828459045=6k+5, so
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I cannot find any reference for this on the internet.
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