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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 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.)