cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A347796 Number of compositions (ordered partitions) of n into at most 3 nonprime parts.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 4, 2, 5, 6, 8, 11, 8, 13, 17, 17, 23, 25, 27, 33, 38, 37, 50, 48, 58, 63, 73, 70, 89, 82, 107, 102, 122, 112, 148, 136, 164, 161, 185, 173, 223, 196, 241, 231, 268, 254, 304, 273, 332, 318, 364, 348, 403, 364, 444, 415, 477, 448, 525, 479, 567
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

Crossrefs

Cf. A018252, A052284, A341480, A347788, A347797, A347798, A347799.

Programs

  • Mathematica
    Table[Length@Flatten[Permutations/@IntegerPartitions[n,3,Select[Range@n,!PrimeQ@#&]],1],{n,0,60}] (* Giorgos Kalogeropoulos, Sep 14 2021 *)

A347797 Number of compositions (ordered partitions) of n into at most 4 nonprime parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 4, 6, 5, 10, 14, 15, 24, 21, 35, 45, 48, 65, 77, 89, 114, 129, 148, 184, 205, 239, 285, 310, 361, 410, 459, 522, 593, 636, 740, 804, 911, 969, 1123, 1169, 1350, 1428, 1595, 1687, 1926, 1974, 2270, 2325, 2611, 2726, 3064, 3120, 3547, 3596, 4012, 4155
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

Crossrefs

Cf. A018252, A052284, A341481, A347788, A347796, A347798, A347799.

Programs

  • Mathematica
    Table[Length@Flatten[Permutations/@IntegerPartitions[n,4,Select[Range@n,!PrimeQ@#&]],1],{n,0,55}] (* Giorgos Kalogeropoulos, Sep 14 2021 *)

A358638 Number of partitions of n into at most 2 distinct nonprime parts.

Original entry on oeis.org

1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 3, 1, 2, 2, 3, 3, 4, 2, 4, 3, 4, 4, 6, 3, 6, 5, 7, 5, 7, 5, 8, 6, 7, 7, 10, 7, 11, 7, 9, 9, 11, 8, 12, 9, 11, 10, 13, 9, 14, 11, 14, 11, 14, 11, 16, 13, 15, 13, 17, 13, 19, 14, 16, 15, 19, 15, 21, 15, 17, 17, 21, 16, 22, 17, 21, 18, 22, 18, 25, 18, 22
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 24 2022

Keywords

Crossrefs

Cf. A005171, A018252, A096258, A302479, A347788, A358639, A358640.

Programs

  • PARI
    A358638(n) = if(n<2,1,!isprime(n)+sum(k=1,(n-1)\2,!(isprime(k)+isprime(n-k)))); \\ Antti Karttunen, Nov 25 2022

Formula

For n > 0, a(n) = A005171(n) + A302479(n).

A347798 Number of compositions (ordered partitions) of n into at most 5 nonprime parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 6, 10, 10, 19, 25, 29, 46, 50, 75, 103, 110, 162, 194, 240, 309, 368, 444, 565, 654, 795, 960, 1106, 1325, 1560, 1792, 2118, 2436, 2785, 3244, 3691, 4194, 4783, 5419, 6121, 6893, 7780, 8617, 9766, 10790, 12060, 13340, 14851, 16231, 18210
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

Crossrefs

Cf. A018252, A052284, A341482, A347788, A347796, A347797, A347799.

Programs

  • Mathematica
    Table[Length@Flatten[Permutations/@IntegerPartitions[n,5,Select[Range@n,!PrimeQ@#&]],1],{n,0,50}] (* Giorgos Kalogeropoulos, Sep 14 2021 *)

A347799 Number of compositions (ordered partitions) of n into at most 6 nonprime parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 5, 6, 10, 16, 19, 31, 44, 52, 86, 101, 148, 206, 237, 350, 441, 551, 743, 900, 1151, 1470, 1782, 2216, 2762, 3287, 4072, 4894, 5835, 7052, 8362, 9856, 11758, 13710, 16066, 18791, 21799, 25271, 29192, 33583, 38485, 44178, 50304
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 14 2021

Keywords

Crossrefs

Cf. A018252, A052284, A341483, A347788, A347796, A347797, A347798.

Programs

  • Mathematica
    Table[Length@Flatten[Permutations/@IntegerPartitions[n,6,Select[Range@n,!PrimeQ@#&]],1],{n,0,46}] (* Giorgos Kalogeropoulos, Sep 14 2021 *)
Showing 1-5 of 5 results.

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