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(Round(c^prime(n)) - 1)/prime(n), where c is the tetranacci constant (A086088).
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%I #26 Dec 23 2024 14:53:43

%S 14,124,390,4118,13690,156122,6351030,22074820,948652694,11818395344,

%T 41868809842,528803858638,24052859078262,1108257471317098,

%U 3982717894786008,185987895674303758,2422894681885464596,8755616404517667662,414985190213435939298

%N (Round(c^prime(n)) - 1)/prime(n), where c is the tetranacci constant (A086088).

%C For n>=4, round(c^prime(n)) == 1 (mod 2*prime(n)). Proof in Shevelev link. In particular, all terms are even.

%H S. Litsyn and V. Shevelev, <a href="http://dx.doi.org/10.1142/S1793042105000339">Irrational Factors Satisfying the Little Fermat Theorem</a>, International Journal of Number Theory, vol.1, no.4 (2005), 499-512.

%H V. Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-March/012750.html">A property of n-bonacci constant</a>, Seqfan (Mar 23 2014)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetranacciConstant.html">Tetranacci Constant</a>

%Y Cf. A007619, A007663, A238693, A238697, A238698, A238700, A086088, A239502.

%K nonn

%O 4,1

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Mar 21 2014