DigitSum

The sum of the digits of n in the given base (default 10).

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaDigit sum↗MathWorldDigitSum↗WikidataQ1363568↗Wolfram LanguageDigitSum✓↗Rosetta CodeSum digits of an integer↗

DigitSum(n)sum of the digits of $n$, base 10.

SageMathsum(Integer(abs(n)).digits(10))SymPysum(digits(abs(n))[1:])

DigitSum(n, base)sum of the digits of $n$ in the given base.

SageMathsum(Integer(abs(n)).digits(base))SymPysum(digits(abs(n), base)[1:])

DigitSum(n, base, k)sum of just the first $k$ digits (most significant first); a negative $k$ sums the last $|k|$ instead (least significant first).

Typed signatures

Type	Package	Applies
(integer, integer?) -> integer	compute-engine	always
(integer, integer?, integer?) -> integer	numeralsreplaces compute-engine	always

Domain: Numeral systems

Details

• Equivalent to summing IntegerDigits(n, base).
• In base 2, the digit sum is the number of set bits (population count).
• $n\equiv\mathrm{DigitSum}(n)\pmod9$ in base 10 -- the basis of the classic divisibility-by-9 check and digital root.
• The sign of n is discarded before summing.

Plot

Examples

3 more kept as data, checked against the oracles

Basic #

live ↗

In$\mathrm{DigitSum}(58\,127)$Out$23$

In base 2 this is the number of set bits

live ↗

In$\mathrm{DigitSum}(58\,127, 2)$Out$9$

Scope #

$255 = \mathrm{ff}_{16}$: $15 + 15$

live ↗

In$\mathrm{DigitSum}(255, 16)$Out$30$

Threads element-wise over a list, as Wolfram's Listable heads do

live ↗

In$\mathrm{DigitSum}(\bigl\lbrack12, 345\bigr\rbrack)$Out$\bigl\lbrack3, 12\bigr\rbrack$

Just the first 4 digits, $6+3+4+5=18$, not the full digit sum (30)

live ↗

In$\mathrm{DigitSum}(6\,345\,354, 10, 4)$Out$18$

Exact digit sum of a roughly thousand-digit integer

live ↗

In$\mathrm{DigitSum}(1+9^{1\,000})$Out$4\,339$

In base 16, $58127=\text{E30F}_{16}$, so $14+3+0+15=32$

live ↗

In$\mathrm{DigitSum}(58\,127, 16)$Out$32$

Threads over a list in base 2

live ↗

In$\mathrm{DigitSum}(\bigl\lbrack6, 7, 2\bigr\rbrack, 2)$Out$\bigl\lbrack2, 3, 1\bigr\rbrack$

Threads over a list of bases

live ↗

In$\mathrm{DigitSum}(7, \bigl\lbrack2, 3, 4\bigr\rbrack)$Out$\bigl\lbrack3, 3, 4\bigr\rbrack$

A negative third argument takes only the last four digits

live ↗

In$\mathrm{DigitSum}(6\,345\,354, 10, -4)$Out$17$

Default base 10: $3+5+2+9+7$

live ↗

In$\mathrm{DigitSum}(35\,297)$Out$26$

Properties #

Digit sum ≡ n (mod 9): the basis of the classic divisibility-by-9 check and the digital root

live ↗

In$\mathrm{DigitSum}(58\,127)\bmod9=58\,127\bmod9$Out$\mathrm{True}$

$3+7+1+0+3$

live ↗

In$\mathrm{DigitSum}(37\,103)$Out$14$

$143=10001111_2$ has five ones

live ↗

In$\mathrm{DigitSum}(143, 2)$Out$5$

The last three digits are all zero

live ↗

In$\mathrm{DigitSum}(123\,000, 10, -3)$Out$0$

Zero has digit sum zero

live ↗

In$\mathrm{DigitSum}(0, 10, -3)$Out$0$

In base 2 the digit sum counts the ones

live ↗

In$\mathrm{DigitSum}(2\,147, 2)$Out$5$

Base 10 digit sum of 2147

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In$\mathrm{DigitSum}(2\,147)$Out$14$

The repunit of 17 ones sums to $17$

live ↗

In$\mathrm{DigitSum}(\frac{10^{17}-1}{9})$Out$17$

A third argument at or above the digit count gives the plain sum

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In$\mathrm{DigitSum}(123\,456, 10, 7)$Out$21$

$263=2023_5$, so the digits add to $7$

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In$\mathrm{DigitSum}(263, 5)$Out$7$

Reversing the digits does not change the sum

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In$\mathrm{DigitSum}(\mathrm{IntegerReverse}(263, 5), 5)$Out$7$

Negative inputs use the absolute value

live ↗

In$\mathrm{DigitSum}(-3\,134)$Out$11$

Possible issues #

live ↗

In$\mathrm{DigitSum}(0)$Out$0$

The sign is discarded

live ↗

In$\mathrm{DigitSum}(-123)$Out$6$

Neat examples #

live ↗

In$\mathrm{DigitSum}(100!)$Out$648$

The digit sum of $2^{1000}$

live ↗

In$\mathrm{DigitSum}(2^{1\,000})$Out$1\,366$

About

Examples	30
Checked against	Wolfram Language 30 agreeSageMath 21 agreeSymPy 21 agreemathlib4 18 agree11 error
Crosswalk	WikipediaMathWorldWikidataWolfram LanguageSageMath ×2SymPy ×2Rosetta Code

Implementation

mappedsagepackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedsympypackages/oracle/src/mappings.ts

mappedsympypackages/oracle/src/mappings.ts

mappedmathlib4packages/oracle/src/mappings.ts

The sum of Nat.digits; natural n only, so a negative n (whose sign ours discards) is a domain error.

mappedmathlib4packages/oracle/src/mappings.ts

As the one-argument row, in an integer base.

mappedmathlib4packages/oracle/src/mappings.ts

The first k digits, most significant first; k past the digit count is the plain sum. A negative k (the last |k| digits) is a domain error, as is a negative n.

See also: DigitCount