A119246 -id:A119246 - cp's OEIS frontend

A052018 Numbers k with the property that the sum of the digits of k is a substring of k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 200, 300, 400, 500, 600, 700, 800, 900, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063

Offset: 1

Patrick De Geest, Nov 15 1999

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A052019, A052020, A052021, A052022, A007953, A005349, A028834.
Cf. A175688. - Reinhard Zumkeller, Aug 15 2010
Cf. A055642, A004426.
Cf. A119246, A138166.

import Data.List (isInfixOf)
a052018 n = a052018_list !! (n-1)
a052018_list = filter f [0..] where
   f x = show (a007953 x) `isInfixOf` show x
-- Reinhard Zumkeller, Jun 18 2013

sdssQ[n_]:=Module[{idn=IntegerDigits[n],s,len},s=Total[idn];len= IntegerLength[ s]; MemberQ[Partition[idn,len,1],IntegerDigits[s]]]; Join[{0},Select[Range[1100],sdssQ]] (* Harvey P. Dale, Jan 02 2013 *)

loop = (str(n) for n in range(399))
print([int(n) for n in loop if str(sum(int(k) for k in n)) in n]) # Jonathan Frech, Jun 05 2017

A138166 Numbers containing their length in their decimal representation.

Original entry on oeis.org

1, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92, 103, 113, 123, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 153, 163, 173, 183, 193, 203, 213, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 243, 253, 263, 273, 283

Offset: 1

Reinhard Zumkeller, Mar 03 2008

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A055642, A138167, A138168.
Cf. A038528 (subsequence).
Cf. A052018, A119246.

import Data.List (isInfixOf)
a138166 n = a138166_list !! (n-1)
a138166_list = filter (\x -> show (a055642 x) `isInfixOf` show x) [0..]
-- Reinhard Zumkeller, Jul 04 2012

A119247 Numbers not containing their digital root in decimal representation.

Original entry on oeis.org

11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 101

Offset: 1

Reinhard Zumkeller, May 10 2006

Complement of A119246.

The ISO human tooth numbering consists of the first 32 terms of this sequence. - Jean-François Alcover, Sep 12 2015

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Digital Root
Wikipedia, Dental notation, section ISO System by the World Health Organization

Cf. A010888.

A119247 := proc(n) option remember: local k: if(n=1)then return 11:fi: for k from procname(n-1)+1 do if(not ((k-1) mod 9) + 1 in convert(convert(k,base,10),set))then return k: fi: od: end: seq(A119247(n), n=1..65); # Nathaniel Johnston, May 05 2011

d[n_] := IntegerDigits[n]; Select[Range[101], FreeQ[d[#1], NestWhile[Total[d[#]] &, #1, # > 9 &]] &] (* Jayanta Basu, Jul 13 2013 *)

A371123 Numbers whose decimal representation contains the digital root of the product of their digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 29, 30, 31, 34, 37, 39, 40, 41, 43, 46, 49, 50, 51, 59, 60, 61, 64, 67, 69, 70, 71, 73, 76, 79, 80, 81, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112

Offset: 1

Saish S. Kambali, Mar 11 2024

All numbers with a 0 digit (A011540) are terms, since their product of digits is 0.

All numbers with a 9 digit (A011539) are terms, since their product of digits is a multiple of 9 and so has digital root 9 if no 0 digits, or 0 if any 0 digit.

			29 is a term because 2*9=18 and 1+8=9 and 29 contains digit 9.

Cf. A007954, A010888, A011539, A011540, A119246.

digRoot[n_] := If[n == 0, 0, Mod[n - 1, 9] + 1]; q[n_] := Module[{d = IntegerDigits[n]}, MemberQ[d, digRoot[Times @@ d]]]; Select[Range[0, 112], q] (* Amiram Eldar, Mar 11 2024 *)

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A052018 Numbers k with the property that the sum of the digits of k is a substring of k.

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A138166 Numbers containing their length in their decimal representation.

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A119247 Numbers not containing their digital root in decimal representation.

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A371123 Numbers whose decimal representation contains the digital root of the product of their digits.

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Mathematica