login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347498 Least k such that there exists an n-element subset S of {1,2,...,k} with the property that all products i * j are distinct for i <= j. 3
1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 17, 19, 20, 23, 25, 28, 29, 31, 33, 37, 40, 41, 42, 43, 47, 51, 53, 55, 57, 59, 61, 67, 69, 71, 73, 75, 79, 83 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= A066720(n) and a(n+1) >= a(n) + 1

LINKS

Table of n, a(n) for n=1..38.

FORMULA

a(n) = min {k >= 1; A338006(k) = n}. - Pontus von Brömssen, Sep 09 2021

EXAMPLE

n | example set

-----+-------------------------------------------------------

1 | {1}

2 | {1, 2}

3 | {1, 2, 3}

4 | {1, 2, 3, 5}

5 | {1, 3, 4, 5, 6}

6 | {1, 3, 4, 5, 6, 7}

7 | {1, 2, 5, 6, 7, 8, 9}

8 | {1, 2, 5, 6, 7, 8, 9, 11}

9 | {1, 2, 5, 6, 7, 8, 9, 11, 13}

10 | {1, 2, 5, 7, 8, 9, 11, 12, 13, 15}

11 | {1, 2, 5, 7, 8, 9, 11, 12, 13, 15, 17}

12 | {1, 2, 5, 7, 8, 9, 11, 12, 13, 15, 17, 19}

13 | {1, 5, 6, 7, 9, 11, 13, 14, 15, 16, 17, 19, 20}

14 | {1, 2, 5, 7, 11, 12, 13, 16, 17, 18, 19, 20, 21, 23}

For n = 4, the set {1,2,3,4} does not have distinct products because 2*2 = 1*4. However, the set {1,2,3,5} does have distinct products because 1*1, 1*2, 1*3, 1*5, 2*2, 2*3, 2*5, 3*3, 3*5, and 5*5 are all distinct.

MATHEMATICA

Table[k=1; While[!Or@@(Length[s=Union[Sort/@Tuples[#, {2}]]]==Length@Union[Times@@@s]&/@Subsets[Range@k, {n}]), k++]; k, {n, 12}] (* Giorgos Kalogeropoulos, Sep 08 2021 *)

PROG

(Python)

from itertools import combinations, combinations_with_replacement

def a(n):

k = n

while True:

for Srest in combinations(range(1, k), n-1):

S = Srest + (k, )

allprods = set()

for i, j in combinations_with_replacement(S, 2):

if i*j in allprods: break

else: allprods.add(i*j)

else: return k

k += 1

print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Sep 08 2021

CROSSREFS

Analogous for sums: A003022 and A227590.

Cf. A066720, A338006, A347499.

Sequence in context: A106843 A057165 A245395 * A023884 A135607 A358221

Adjacent sequences: A347495 A347496 A347497 * A347499 A347500 A347501

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Sep 03 2021

EXTENSIONS

a(15)-a(20) from Michael S. Branicky, Sep 08 2021

a(21)-a(38) (based on the terms in A338006) from Pontus von Brömssen, Sep 09 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)