A319651 -id:A319651 - cp's OEIS frontend

A319803 a(n) = A319651(n) + A038574(n).

0, 2, 4, 4, 8, 12, 8, 12, 16, 10, 16, 26, 16, 26, 36, 26, 36, 42, 20, 26, 32, 26, 36, 42, 32, 42, 52, 28, 40, 68, 40, 52, 80, 68, 80, 92, 40, 52, 80, 52, 80, 108, 80, 108, 120, 68, 80, 92, 80, 108, 120, 92, 120, 132, 56, 68, 80, 68, 80, 92, 80, 92, 104, 68, 80, 92, 80, 108, 120, 92, 120, 132, 80, 92

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055946.

Seiichi Manyama, Table of n, a(n) for n = 0..6560

Base b: A319785 (b=2), this sequence (b=3), A319804 (b=4), A319805 (b=5), A319806 (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055946, A038574, A319651.

Table[FromDigits[Reverse[#], 3] + FromDigits[#, 3] & [Sort[IntegerDigits[n, 3]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 3)); fromdigits(vecsort(nd), 3) + fromdigits(vecsort(nd,,4), 3); \\ Michel Marcus, Sep 28 2018

A319722 Write n in 5-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 11, 16, 21, 10, 11, 12, 17, 22, 15, 16, 17, 18, 23, 20, 21, 22, 23, 24, 25, 30, 55, 80, 105, 30, 31, 56, 81, 106, 55, 56, 61, 86, 111, 80, 81, 86, 91, 116, 105, 106, 111, 116, 121, 50, 55, 60, 85, 110, 55, 56, 61, 86, 111, 60, 61, 62, 87, 112, 85

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..3124

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), this sequence (b=5), A319723 (b=6), A319724 (b=7), A319725 (b=8), A319726 (b=9), A004186 (b=10).

Cf. A165032, A319653.

Table[FromDigits[ReverseSort[IntegerDigits[n, 5]], 5], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 5), , 4), 5); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(5, 100)

n <= a(n) < 5n. - Charles R Greathouse IV, Aug 07 2024

A319723 Write n in 6-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 13, 19, 25, 31, 12, 13, 14, 20, 26, 32, 18, 19, 20, 21, 27, 33, 24, 25, 26, 27, 28, 34, 30, 31, 32, 33, 34, 35, 36, 42, 78, 114, 150, 186, 42, 43, 79, 115, 151, 187, 78, 79, 85, 121, 157, 193, 114, 115, 121, 127, 163, 199, 150, 151, 157, 163

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..7775

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), A319722 (b=5), this sequence (b=6), A319724 (b=7), A319725 (b=8), A319726 (b=9), A004186 (b=10).

Cf. A165051, A319654.

Table[FromDigits[ReverseSort[IntegerDigits[n, 6]], 6], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 6), , 4), 6); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(6, 100)

n <= a(n) < 6n. - Charles R Greathouse IV, Aug 07 2024

A319724 Write n in 7-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 15, 22, 29, 36, 43, 14, 15, 16, 23, 30, 37, 44, 21, 22, 23, 24, 31, 38, 45, 28, 29, 30, 31, 32, 39, 46, 35, 36, 37, 38, 39, 40, 47, 42, 43, 44, 45, 46, 47, 48, 49, 56, 105, 154, 203, 252, 301, 56, 57, 106, 155, 204, 253, 302, 105, 106, 113, 162

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..2400

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), A319722 (b=5), A319723 (b=6), this sequence (b=7), A319725 (b=8), A319726 (b=9), A004186 (b=10).

Cf. A165071, A319655.

Table[FromDigits[ReverseSort[IntegerDigits[n, 7]], 7], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 7), , 4), 7); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(7, 100)

n <= a(n) < 7n. - Charles R Greathouse IV, Aug 07 2024

A319726 Write n in 9-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 28, 37, 46, 55, 64, 73, 18, 19, 20, 29, 38, 47, 56, 65, 74, 27, 28, 29, 30, 39, 48, 57, 66, 75, 36, 37, 38, 39, 40, 49, 58, 67, 76, 45, 46, 47, 48, 49, 50, 59, 68, 77, 54, 55, 56, 57, 58, 59, 60, 69, 78, 63, 64, 65, 66, 67, 68, 69

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..6560

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), A319722 (b=5), A319723 (b=6), A319724 (b=7), A319725 (b=8), this sequence (b=9), A004186 (b=10).

Cf. A165110, A319657.

Table[FromDigits[Reverse[Sort[IntegerDigits[n,9]]],9],{n,0,70}] (* Harvey P. Dale, Oct 26 2022 *)

a(n) = fromdigits(vecsort(digits(n, 9), , 4), 9); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(9, 100)

n <= a(n) < 9n. - Charles R Greathouse IV, Aug 07 2024

A319720 Write n in 4-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 9, 13, 8, 9, 10, 14, 12, 13, 14, 15, 16, 20, 36, 52, 20, 21, 37, 53, 36, 37, 41, 57, 52, 53, 57, 61, 32, 36, 40, 56, 36, 37, 41, 57, 40, 41, 42, 58, 56, 57, 58, 62, 48, 52, 56, 60, 52, 53, 57, 61, 56, 57, 58, 62, 60, 61, 62, 63, 64, 80, 144, 208, 80, 84

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..4095

b-ary: A073138 (b=2), A319651 (b=3), this sequence (b=4), A319722 (b=5), A319723 (b=6), A319724 (b=7), A319725 (b=8), A319726 (b=9), A004186 (b=10).

Cf. A165012, A319652.

Table[FromDigits[ReverseSort[IntegerDigits[n, 4]], 4], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 4), , 4), 4); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(4, 100)

n <= a(n) < 4n. - Charles R Greathouse IV, Aug 07 2024

A319725 Write n in 8-ary, sort digits into decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 25, 33, 41, 49, 57, 16, 17, 18, 26, 34, 42, 50, 58, 24, 25, 26, 27, 35, 43, 51, 59, 32, 33, 34, 35, 36, 44, 52, 60, 40, 41, 42, 43, 44, 45, 53, 61, 48, 49, 50, 51, 52, 53, 54, 62, 56, 57, 58, 59, 60, 61, 62, 63, 64, 72, 136, 200, 264

Offset: 0

Seiichi Manyama, Sep 26 2018

Seiichi Manyama, Table of n, a(n) for n = 0..4095

b-ary: A073138 (b=2), A319651 (b=3), A319720 (b=4), A319722 (b=5), A319723 (b=6), A319724 (b=7), this sequence (b=8), A319726 (b=9), A004186 (b=10).

Cf. A165090, A319656.

Table[FromDigits[ReverseSort[IntegerDigits[n, 8]], 8], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = fromdigits(vecsort(digits(n, 8), , 4), 8); \\ Michel Marcus, Sep 26 2018

def A(k, n)
  (0..n).map{|i| i.to_s(k).split('').sort.reverse.join.to_i(k)}
end
p A(8, 100)

n <= a(n) < 8n. - Charles R Greathouse IV, Aug 07 2024

A351988 In the factorial base expansion of n, arrange digits in decreasing order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 8, 9, 14, 15, 12, 14, 14, 15, 16, 17, 18, 20, 20, 21, 22, 23, 24, 30, 30, 32, 54, 56, 30, 32, 32, 33, 56, 57, 54, 56, 56, 57, 62, 63, 78, 80, 80, 81, 86, 87, 48, 54, 54, 56, 60, 62, 54, 56, 56, 57, 62, 63, 60, 62, 62, 63, 64, 65, 84, 86

Offset: 0

Rémy Sigrist, Feb 27 2022

This sequence is to factorial base what A004186 is to decimal base.

			For n = 1664:
- the factorial base expansion of 1664 is "214110",
- arranging these digits in decreasing order gives "421110",
- so a(1664) = 4*6! + 2*5! + 1*4! + 1*3! + 1*2! + 0*1! = 3152.

Cf. A004186 (decimal analog), A073138 (binary analog), A108731, A319651 (ternary analog), A351987.

max = 5; b = MixedRadix[Range[max, 2, -1]]; a[n_] := FromDigits[Sort[IntegerDigits[n, b], Greater], b]; Array[a, max!, 0] (* Amiram Eldar, Feb 28 2022 *)

a(n) = { my (dd=[]); for (r=2, oo, if (n==0, dd = vecsort(dd); return (sum(k=1, #dd, dd[k]*k!)), dd = concat(dd, n%r); n\=r)) }

a(a(n)) = a(n).

a(n) >= n with equality iff n belongs to A351987.

cp's OEIS Frontend

A319803 a(n) = A319651(n) + A038574(n).

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A319722 Write n in 5-ary, sort digits into decreasing order.

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A319723 Write n in 6-ary, sort digits into decreasing order.

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A319724 Write n in 7-ary, sort digits into decreasing order.

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A319726 Write n in 9-ary, sort digits into decreasing order.

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A319720 Write n in 4-ary, sort digits into decreasing order.

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A319725 Write n in 8-ary, sort digits into decreasing order.

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Mathematica

PARI

Ruby

Formula

A351988 In the factorial base expansion of n, arrange digits in decreasing order.

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