A327453 -id:A327453 - cp's OEIS frontend

A327456 Lexicographically earliest sequence of distinct positive numbers such that if we add six successive digits the result is divisible by 6.

1, 2, 3, 4, 5, 9, 7, 8, 34, 53, 12, 94, 59, 18, 345, 31, 23, 45, 37, 29, 453, 72, 945, 91, 83, 459, 78, 3453, 123, 4531, 89, 4537, 234, 531, 294, 537, 834, 591, 894, 597, 2345, 97, 2945, 312, 3459, 129, 4591, 8345, 318, 9453, 183, 4597, 8945, 372, 9459, 189

Offset: 1

N. J. A. Sloane, Sep 22 2019

Éric Angelini, Posting to Sequence Fans Mailing List, Sep 16 2019.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A327456

Cf. A327453-A327455.

PARI
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See Links section.
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More terms from Rémy Sigrist, Sep 22 2019

A327454 Lexicographically earliest sequence of distinct positive numbers such that if we add four successive digits the result is divisible by 4.

Original entry on oeis.org

1, 2, 3, 6, 5, 23, 21, 27, 25, 63, 29, 67, 61, 232, 9, 236, 12, 7, 65, 272, 16, 32, 52, 36, 56, 72, 92, 76, 96, 321, 276, 123, 69, 632, 127, 212, 325, 636, 163, 216, 329, 672, 167, 252, 361, 676, 523, 256, 365, 2321, 2325, 2329, 2361, 2365, 2369, 2721, 2725

Offset: 1

N. J. A. Sloane, Sep 22 2019

Éric Angelini, Posting to Sequence Fans Mailing List, Sep 16 2019.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A327454

Cf. A327453-A327456.

PARI
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See Links section.
```

More terms from Rémy Sigrist, Sep 22 2019

A327455 Lexicographically earliest sequence of distinct positive numbers such that if we add five successive digits the result is divisible by 5.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 51, 23, 40, 12, 34, 56, 28, 45, 17, 39, 512, 84, 517, 89, 562, 340, 62, 345, 67, 390, 123, 90, 128, 95, 173, 401, 73, 406, 78, 451, 234, 567, 395, 178, 456, 239, 5123, 901, 284, 5128, 906, 289, 5173, 951, 734, 5178, 956, 739, 5623

Offset: 1

N. J. A. Sloane, Sep 22 2019

Éric Angelini, Posting to Sequence Fans Mailing List, Sep 16 2019.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A327455

Cf. A327453-A327456.

PARI
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See Links section.
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More terms from Rémy Sigrist, Sep 22 2019

A327733 Lexicographically earliest sequence of distinct positive numbers such that if we add eight successive digits the result is divisible by 8.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 41, 23, 45, 67, 49, 234, 56, 74, 9, 2345, 674, 12, 34, 567, 412, 345, 6741, 23456, 741, 234567, 492, 3456, 749, 2345674, 92, 34567, 4123, 456, 7412, 345674, 123, 4567, 4923, 45674, 923, 456741, 23456741, 23456749, 234567412, 3456741

Offset: 1

Rémy Sigrist, Sep 23 2019

This sequence has interesting graphical features.

The infinite string resulting from the concatenation of all terms matches the regular expression "^([19]2345674)*".

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A327733

See A327453 and A327735 for other variants.

PARI
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See Links section.
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A327735 Lexicographically earliest sequence of distinct positive numbers such that if we add ten successive digits the result is divisible by 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 51, 23, 45, 67, 89, 512, 34, 56, 78, 95, 12, 345, 678, 951, 234, 567, 895, 123, 456, 789, 5123, 4567, 8951, 2345, 6789, 51234, 5678, 9512, 3456, 7895, 1234, 56789, 512345, 67895, 12345, 678951, 23456, 78951, 234567, 89512, 34567

Offset: 1

Rémy Sigrist, Sep 23 2019

The infinite string resulting from the concatenation of all terms matches the regular expression "^(1234567895)*".

Rémy Sigrist, PARI program for A327735
Rémy Sigrist, Logarithmic scatterplot of the first 500 terms

See A327453 and A327733 for other variants.

PARI
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See Links section.
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Apparently, a(n + 100) = a(n) * 10^10 + (a(n) mod 10^10) for any n >= 90.

cp's OEIS Frontend

A327456 Lexicographically earliest sequence of distinct positive numbers such that if we add six successive digits the result is divisible by 6.

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A327454 Lexicographically earliest sequence of distinct positive numbers such that if we add four successive digits the result is divisible by 4.

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A327455 Lexicographically earliest sequence of distinct positive numbers such that if we add five successive digits the result is divisible by 5.

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References

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Programs

PARI

Extensions

A327733 Lexicographically earliest sequence of distinct positive numbers such that if we add eight successive digits the result is divisible by 8.

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PARI

A327735 Lexicographically earliest sequence of distinct positive numbers such that if we add ten successive digits the result is divisible by 10.

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