A030127 Term at which n-Somos sequence first becomes nonintegral.

17, 19, 20, 22, 24, 27, 28, 30, 33, 34, 36, 39, 41, 42, 44, 46, 48, 51, 52, 55, 56, 58, 60, 62, 65, 66, 68, 70, 72, 75, 76, 78, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 107, 108, 110, 112, 114, 116, 118, 120, 123, 124, 126, 129, 130, 132, 134, 136, 138

Offset: 8

Author

Eric W. Weisstein

Keywords

• nonn

Comments

A101591 lists the positions of the odd terms. - Paul D. Hanna, Dec 08 2004

Conjecture: for even terms, a(n) = 2*n, else a(n) = 2*n+1 when n is in A101591. - Paul D. Hanna, Dec 08 2004

There does not seem to be a published proof that a(n) is defined for all n>=8. - Michael Somos, Jul 19 2014

Links

• Ralph H. Buchholz and Randall L. Rathbun, An infinite set of Heron triangles with two rational medians, The American Mathematical Monthly, Vol. 104, No. 2 (Feb., 1997), pp. 107-115.
• Harini Desiraju and Brady Haran, The Troublemaker Number, Numberphile video (2022).
• David Gale, The strange and surprising saga of the Somos sequences, Math. Intelligencer 13(1) (1991), pp. 40-42.
• J. L. Malouf, An integer sequence from a rational recursion, Discr. Math. 110 (1992), 257-261.
• R. M. Robinson, Periodicity of Somos sequences, Proc. Amer. Math. Soc., 116 (1992), 613-619.
• Eric Weisstein's World of Mathematics, Somos Sequence.

Crossrefs

Cf. A101591.

Extensions

More terms from Paul D. Hanna, Dec 08 2004