A125290 -id:A125290 - cp's OEIS frontend

A061827 Number of partitions of n into parts which are the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 4, 3, 3, 3, 3, 1, 11, 1, 4, 7, 3, 5, 2, 4, 2, 1, 11, 6, 1, 3, 3, 7, 2, 2, 5, 1, 11, 11, 4, 1, 3, 4, 2, 7, 2, 1, 11, 6, 4, 3, 1, 2, 2, 2, 2, 1, 11, 11, 11, 6, 3, 1, 2, 3, 4, 1, 11, 6, 4, 3, 3, 2, 1, 2, 2, 1, 11, 11, 4, 11, 3, 4, 2, 1, 2, 1, 11, 6, 11, 3, 3, 6, 2, 2

Offset: 1

Amarnath Murthy, May 28 2001

a(A125289(n)) = 1, a(A125290(n)) > 1.

			For n = 11, 1+1+1+1+1+1+1+1+1+1+1. so a(11) = 1. For n = 12, 2+2+2+2+2+2 = 2+2+1+1+1+1+1+1+1+1 = ...etc
a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.

Alois P. Heinz, Table of n, a(n) for n = 1..15000 (first 1250 terms from Reinhard Zumkeller)

Cf. A061828, A109950, A119999, A125291, A136460, A193513.

import Data.List (sort, nub)
import Data.Char (digitToInt)
a061827 n =
   p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where
      p _ []        = 0
      p 0 _         = 1
      p m ds'@(d:ds)
        | m < d     = 0
        | otherwise = p (m - d) ds' + p m ds
-- Reinhard Zumkeller, Aug 01 2011

Length[IntegerPartitions[#,All,DeleteDuplicates@DeleteCases[IntegerDigits[#],0]]]&/@Range[200] (* Sander G. Huisman, Nov 14 2022 *)

More terms from David Wasserman, Jul 29 2002

A101594 Numbers with exactly two distinct decimal digits, neither of which is 0.

Original entry on oeis.org

12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 98, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131

Offset: 1

David Wasserman, Dec 07 2004

First differs from A125290 at a(83) = 131 != 123 = A101594(83). - Michael S. Branicky, Dec 13 2021

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A083985, A031955, A004719, A043537, A168046.

Subsequence of A052382, A125290.

a101594 n = a101594_list !! (n-1)
a101594_list = filter ((== 2) . a043537) a052382_list
-- Reinhard Zumkeller, Jun 18 2013

Select[Range[200], FreeQ[#, 0] && Length[Union[#]] == 2 & [IntegerDigits[#]] &] (* Paolo Xausa, May 06 2024 *)

def ok(n): s = set(str(n)); return len(s) == 2 and "0" not in s
print([k for k in range(132) if ok(k)]) # Michael S. Branicky, Dec 13 2021

A168046(a(n)) * A043537(A004719(a(n))) = 2. - Reinhard Zumkeller, Jun 18 2013

A125293 Numbers with at least one 1 and one 2 in ternary representation.

Original entry on oeis.org

5, 7, 11, 14, 15, 16, 17, 19, 21, 22, 23, 25, 29, 32, 33, 34, 35, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 83, 86, 87, 88, 89, 92, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106

Offset: 1

Reinhard Zumkeller, Nov 26 2006

Complement of A125292; A062756(a(n))*A081603(a(n)) > 0;

A125291(a(n)) > 1.

Eric Weisstein's World of Mathematics, Ternary
Index entries for 3-automatic sequences.

Cf. A007089, A125290.

Select[Range[120],DigitCount[#,3,1]>0&&DigitCount[#,3,2]>0&] (* Harvey P. Dale, Apr 12 2013 *)

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A061827 Number of partitions of n into parts which are the digits of n.

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A101594 Numbers with exactly two distinct decimal digits, neither of which is 0.

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A125293 Numbers with at least one 1 and one 2 in ternary representation.

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