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 A180928 1 + product of any two terms is a triangular number. 1
 0, 1, 5, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence could also start 0, 1, 2, 27, ... - R. J. Mathar, Oct 03 2010 This sequence is also finite and complete. - Max Alekseyev, Feb 16 2011 If 1*x+1, 5*x+1, 27*x+1 are triangular numbers, then 8*x+9=p^2, 40*x+9=q^2, 216*x+9=r^2 for some integers p,q,r. They should also satisfy the system of equations { 5*p^2 - q^2 = 36, 27*p^2 - r^2 = 234 } which has no integer solutions. See Alekseyev, 2011. A192225 contains another result from the same paper. LINKS Max A. Alekseyev (2011). On the Intersections of Fibonacci, Pell, and Lucas Numbers, INTEGERS 11(3), pp. 239-259. doi:10.1515/INTEG.2011.021 EXAMPLE (0*1)+1 = 1 is triangular. (0*5)+1 = 1 is triangular. (1*5)+1 = 6 is triangular. (0*27)+1 = 1 is triangular. (1*27)+1 = 28 is triangular. (5*27)+1 = 136 is triangular. (0*70)+1 = 1 is triangular. (1*70)+1 = 71 is NOT triangular, so 70 is not the next value. (5*70)+1 = 351 is triangular. (27*70)+1 = 1891 is triangular. CROSSREFS This is to A030063 as A000217 is to A000290. Sequence in context: A281747 A064489 A081089 * A118391 A196085 A097088 Adjacent sequences:  A180925 A180926 A180927 * A180929 A180930 A180931 KEYWORD nonn,full,fini AUTHOR Jonathan Vos Post, Sep 25 2010 EXTENSIONS No further terms below 10^20. - Charles R Greathouse IV, Sep 29 2010 Keywords 'full', 'fini' from Max Alekseyev, Feb 16 2011 STATUS approved

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)