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 A135435 a(n) = a(n-4) + a(n-7) with a(0), ..., a(6) = [7,0,0,0,4,0,0]. 2

%I

%S 7,0,0,0,4,0,0,7,4,0,0,11,4,0,7,15,4,0,18,19,4,7,33,23,4,25,52,27,11,

%T 58,75,31,36,110,102,42,94,185,133,78,204,287,175,172,389,420,253,376,

%U 676,595,425,765,1096,848,801,1441,1691,1273,1566,2537,2539,2074,3007,4228

%N a(n) = a(n-4) + a(n-7) with a(0), ..., a(6) = [7,0,0,0,4,0,0].

%C Of interest because {7,11} is the earliest pair of typical primes belonging to a single hexad. Herein "pseudoprime" means sequence-specific psp. (i.e. dividing its term with rem. 0), not general number-theoretic psp. The only psp.s of concern, from the standpoint of primality testing, being those congruent to 1 or 5 (mod 6), are the six quadratics of the present zero-termed primes 5,13,17 the only relevant psp.s of this sequence? Or are there additional examples > 289?

%H G. C. Greubel, <a href="/A135435/b135435.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1, 0, 0, 1).

%F G.f.: (7-3*x^4)/(1-x^4-x^7). - _R. J. Mathar_, Oct 24 2009

%t LinearRecurrence[{0,0,0,1,0,0,1},{7,0,0,0,4,0,0},70] (* _Harvey P. Dale_, Jan 20 2013 *)

%o (PARI) Vec((7-3*x^4)/(1-x^4-x^7) + O(x^80)) \\ _Michel Marcus_, Oct 14 2016

%Y Cf. A133394.

%K easy,nonn

%O 0,1

%A G. Reed Jameson (Reedjameson(AT)yahoo.com), Dec 13 2007, Dec 16 2007

%E More terms from _R. J. Mathar_, Oct 24 2009

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Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)