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A274696 Variation on Fermat's Diophantine m-tuple: 1 + the LCM of any two distinct terms is a square. 0
0, 1, 3, 8, 15, 24, 120, 168, 840, 1680, 5040, 201600, 256032000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(1) = 0; for n>1, a(n) = smallest integer > a(n-1) such that lcm(a(n),a(i))+1 is square for all 1 <= i <= n-1.

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

After a(1)=0, a(2)=1, a(3)=3, we want m, the smallest number > 3 such that lcm(0,m)+1, lcm(2,m)+1 and lcm(3,m)+1 are squares: this is m = 8 = a(4).

MATHEMATICA

a = {0}; Do[AppendTo[a, SelectFirst[Range[Max@ a + 1, 3*10^5], Function[k, Times @@ Boole@ Map[IntegerQ@ Sqrt[LCM[a[[#]], k] + 1] &, Range[n - 1]] == 1]]], {n, 2, 12}]; a (* Michael De Vlieger, Jul 05 2016, Version 10 *)

PROG

(Sage)

seq = [0]

prev_element = 0

max_n = 13

for n in range(2, max_n+1):

    next_element = prev_element + 1

    while True:

        all_match = True

        for element in seq:

            x = lcm( element, next_element ) + 1

            if not is_square(x):

                all_match = False

                break

        if all_match:

            seq.append( next_element )

            print(seq)

            break

        next_element += 1

    prev_element = next_element

print(seq)

CROSSREFS

Cf. A030063.

Sequence in context: A173569 A173570 A060615 * A022451 A212772 A238806

Adjacent sequences:  A274693 A274694 A274695 * A274697 A274698 A274699

KEYWORD

nonn

AUTHOR

Robert C. Lyons, Jul 05 2016

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)