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A338973 Possible number of digits in a factorial.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 81, 82, 84, 86, 88, 90, 91, 93, 95, 97, 99, 101, 102

Offset: 1

Christian Amet, Dec 18 2020

This is A034886 with duplicate terms removed.

Cf. A000142, A034886.

DeleteDuplicates @ IntegerLength[Range[71]!] (* Amiram Eldar, Dec 24 2020 *)

a(n) = A034886(n+3) for n>=4.

A176423 Numbers that are the sum of at least three distinct nonnegative integers in arithmetic progression.

Original entry on oeis.org

3, 6, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Offset: 1

Christian Amet, Apr 17 2010

According to the theorem in the December 1996 issue of Le Petit Vert, these numbers consist of 3, 6 and the composite numbers greater than 8. - Peter Munn, Aug 20 2024

Ray Chandler, Table of n, a(n) for n = 1..10000
Le Petit Vert, Problem 47, p.20, September 1996. (in French)
Le Petit Vert, Solution of problem 47, pp. 21-22, December 1996. (in French)

Cf. A002808.

Extended by Ray Chandler, Mar 23 2016

A120433 Numbers whose Roman numeral representation uses the subtractive notation.

Original entry on oeis.org

4, 9, 14, 19, 24, 29, 34, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 59, 64, 69, 74, 79, 84, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 109, 114, 119, 124, 129, 134, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154, 159, 164, 169, 174

Offset: 1

Christian Amet, Jul 13 2006

Each number in this sequence has a 4 or a 9 in its decimal representation, corresponding to one of IV, IX, XL, XC, CD, CM. - Alonso del Arte, Jan 05 2018

			In Roman numerals, 14 is XIV, that is, X + (V - I) = 10 + (5 - 1) = 14, so 14 is in the sequence.
In Roman numerals, 15 is XV, meaning X + V = 10 + 5 = 15, which does not use subtractive notation, so 15 is not in the sequence.

Nathaniel Johnston, Table of n, a(n) for n = 1..1952 (complete up to 3999)

Cf. A061493.

Cf. A016897, 5n + 4 (first diverges after 39, as that sequence does not include 40, 41, 42, 43).

with(StringTools): for n from 1 to 300 do r:=convert(n,roman): if(Search("IV",r)>0 or Search("IX",r)>0 or Search("XL",r)>0 or Search("XC",r)>0 or Search("CD",r)>0 or Search("CM",r)>0)then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Select[Range[3999], StringContainsQ[RomanNumeral[#], {"IV", "IX", "XL", "XC", "CD", "CM"}] &] (* Michael De Vlieger, Aug 20 2024 *)

def ok(n): return {"4", "9"} & set(str(n))
afull = [k for k in range(4000) if ok(k)] # Michael S. Branicky, Aug 20 2024

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User: Christian Amet

A338973 Possible number of digits in a factorial.

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A176423 Numbers that are the sum of at least three distinct nonnegative integers in arithmetic progression.

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A120433 Numbers whose Roman numeral representation uses the subtractive notation.

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