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 A239566 (Round(c^prime(n)) - 1)/prime(n), where c is the heptanacci constant (A118428). 2
 7200, 25562, 332466, 16472758, 61145666, 3200477798, 45473543628, 172043098818, 2478186385762, 137291966046470, 7704742900338106, 29569459376703894, 1681851263230158754, 24987922624169214866, 96433670513455876108, 5566902760779797458210 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,1 COMMENTS For n>=7, round(c^prime(n)) == 1 (mod 2*prime(n)). Proof in Shevelev link. In particular, all terms are even. LINKS S. Litsyn and V. Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499-512. V. Shevelev, A property of n-bonacci constant, Seqfan (Mar 23 2014) Eric Weisstein's World of Mathematics, Heptanacci Constant FORMULA All roots of the equation x^7-x^6-x^5-x^4-x^3-x^2-x-1 = 0 are the following: c=1.9919641966050350211, -0.78418701799584451319 +/- 0.36004972226381653409*i, -0.24065633852269642508 + /- 0.84919699909267892575*i, 0.52886125821602342773 +/- 0.76534196109589443115*i. Absolute values of all roots, except for septanacci constant c, are less than 1. Conjecture. Absolute values of all roots of the equation x^n - x^(n-1) - ... -x - 1 = 0, except for n-bonacci constant c_n, are less than 1. If the conjecture is valid, then for sufficiently large k=k(n), for all m>=k, we have round(c_n^prime(m)) == 1 (mod 2*prime(m)) (cf. Shevelev link). CROSSREFS Cf. A007619, A007663, A238693, A238697, A238698, A238700, A239502, A239544, A239564, A239565. Sequence in context: A204480 A035906 A190114 * A236993 A218513 A181259 Adjacent sequences: A239563 A239564 A239565 * A239567 A239568 A239569 KEYWORD nonn AUTHOR Peter J. C. Moses and Vladimir Shevelev, Mar 21 2014 STATUS approved

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Last modified December 3 20:51 EST 2022. Contains 358543 sequences. (Running on oeis4.)