

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

Table of n, a(n) for n=7..22.
S. Litsyn and V. Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499512.
V. Shevelev, A property of nbonacci constant, Seqfan (Mar 23 2014)
Eric Weisstein's World of Mathematics, Heptanacci Constant


FORMULA

All roots of the equation x^7x^6x^5x^4x^3x^2x1 = 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^(n1)  ... x  1 = 0, except for nbonacci 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: A064979 A204480 A190114 * A236993 A035906 A218513
Adjacent sequences: A239563 A239564 A239565 * A239567 A239568 A239569


KEYWORD

nonn


AUTHOR

Peter J. C. Moses and Vladimir Shevelev, Mar 21 2014


STATUS

approved



