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# Template:Integer sequence

Use the {{intseq}} (or {{integer sequence}}) OEIS Wiki utility template to get a standardized presentation of integer sequences. The template adds the opening and closing braces automatically.

Note: for your convenience, the template converts hyphens “-” to minus signs “−” and then appends a 1 mu (mathematical unit) space before 0, 4, 6 or 9.

## Usage

{{intseq|integer sequence}}

or

{{intseq|integer sequence|roman}}

## Examples

The code:

```: {{intseq||roman}}
```

yields the default [Roman] integer sequence:

{I, II, III, IV, V, VI, VII, VIII, IX, X, ...}

The code:

```: {{intseq}}
```

yields the default [Hindu-Arabic] integer sequence:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...}

The code:

```: {{intseq|II, III, V, VII, XI, XIII, XVII, IXX, XXIII, IXXX, XXXI, ...|roman}}
```

yields:

{II, III, V, VII, XI, XIII, XVII, IXX, XXIII, IXXX, XXXI, ...}

The code:

```A006577 Number of halving and tripling steps to reach {{mathfont|1}} in [[3x+1 problem|{{'|{{mathfont|3{{sp|1}}''x'' + 1}}|'}} problem]], or {{mathfont|−1}} if {{mathfont|1}} is never reached.

: {{intseq|0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, 7, 15, 15, 10, 23, 10, 111, 18, 18, 18, 106, 5, 26, 13, 13, 21, 21, 21, 34, 8, 109, 8, 29, 16, 16, 16, 104, 11, 24, 24, 24, 11, 11, 112, 112, 19, 32, 19, 32, ...}}

A061641 Pure numbers in the Collatz ({{math|3{{sp|1}}''x'' + 1|tex = 3x + 1|&}}) iteration. Also called [[pure hailstone numbers]], i.e. those which do not occur in the trajectories of smaller numbers.

: {{intseq|0, 1, 3, 6, 7, 9, 12, 15, 18, 19, 21, 24, 25, 27, 30, 33, 36, 37, 39, 42, 43, 45, 48, 51, 54, 55, 57, 60, 63, 66, 69, 72, 73, 75, 78, 79, 81, 84, 87, 90, 93, 96, 97, 99, 102, 105, 108, 109, 111, 114, 115, 117, 120, 123, ...}}
```

yields:

A006577 Number of halving and tripling steps to reach 1 in 3 x + 1’ problem, or −1 if 1 is never reached.

{0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, 7, 7, 15, 15, 10, 23, 10, 111, 18, 18, 18, 106, 5, 26, 13, 13, 21, 21, 21, 34, 8, 109, 8, 29, 16, 16, 16, 104, 11, 24, 24, 24, 11, 11, 112, 112, 19, 32, 19, 32, ...}
A061641 Pure numbers in the Collatz (
 3 x + 1
) iteration. Also called pure hailstone numbers, i.e. those which do not occur in the trajectories of smaller numbers.
{0, 1, 3, 6, 7, 9, 12, 15, 18, 19, 21, 24, 25, 27, 30, 33, 36, 37, 39, 42, 43, 45, 48, 51, 54, 55, 57, 60, 63, 66, 69, 72, 73, 75, 78, 79, 81, 84, 87, 90, 93, 96, 97, 99, 102, 105, 108, 109, 111, 114, 115, 117, 120, 123, ...}

The code (using hyphens):

```A108911: Difference between {{math|''n''|tex = n|&}} and the sum of the [[factorials]] of its [[decimal]] digits.

: {{intseq|0, 0, -3, -20, -115, -714, -5033, -40312, -362871, 8, ...}}
```

yields (hyphens converted to minus signs):

A108911: Difference between
 n
and the sum of the factorials of its decimal digits.
{0, 0, −3, −20, −115, −714, −5033, − 40312, −362871, 8, ...}

The code:

```A129250 Class {{math|16{{sym|-}}|&}} primes. {{intseq|22111003847, 25782283783, 34824831403, 42970472971, 44905511759, 45490491349, 52486961911, 54560052479, 55437374381, 65803884467, 66333011539, ...}}
```

yields

A129250 Class
 16−
primes.
{22111003847, 25782283783, 34824831403, 42970472971, 44905511759, 45490491349, 52486961911, 54560052479, 55437374381, 65803884467, 66333011539, ...}

## Test

For testing only: it is simpler to just use hyphens instead of {{op|-}}.

The code:

```A108911: Difference between {{math|''n''|tex = n|&}} and the sum of the [[factorials]] of its [[decimal]] digits.

: {{intseq|0, 0, {{op|-}}3, {{op|-}}20, {{op|-}}115, {{op|-}}714, {{op|-}}5033, {{op|-}}40312, {{op|-}}362871, 8, ...}}
```

yields:

A108911: Difference between
 n
and the sum of the factorials of its decimal digits.
{0, 0, −3, −20, −115, −714, −5033, −40312, −362871, 8, ...}