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A133394 a(n)=a(n-2)+a(n-5). 4

%I

%S 0,2,0,2,5,2,7,2,9,7,11,14,13,23,20,34,34,47,57,67,91,101,138,158,205,

%T 249,306,387,464,592,713,898,1100,1362,1692,2075,2590,3175,3952,4867,

%U 6027,7457,9202,11409,14069,17436,21526,26638,32935,40707,50371,62233

%N a(n)=a(n-2)+a(n-5).

%C Perrin-like prime-divisibility sequence, but based upon template 7=5+2 in place of 5=3+2.

%C 1. Apparently identical to A007387 but for latter's third term 3. 2. Attention directed to remainder upon division of a term by its (composite) argument, when latter =1 or 5 (mod 6). Possible factorization tool for impostor candidate primes? 3. Recurrence period, any length-five string of term values (mod 6) found in the sequence: 2^3*13*31, to Perrin's three-term period of 7*13. Note 13= 2*6+1, 31 = 5*6+1. 4. Query: Smallest pseudoprime >9. 5. Query: Closed form for n-th term.

%C Semiprimes a= 9, 14, 34, 57, 91 etc. are at the indices n=9, 12, 16, 17, 19, 21, 24, 25, 26, 31, 32, 40, 44, 45, 51, 53, 59, 66, 72, 76, 80, 110 etc. - _R. J. Mathar_, Nov 24 2007

%H Harvey P. Dale, <a href="/A133394/b133394.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1).

%F O.g.f.: -x*(2+5*x^3)/(-1+x^2+x^5). - _R. J. Mathar_, Nov 24 2007

%F Rewritten, Mathar's o.g.f. resembles a logarithmic derivative: -(5*x^4 + 2*x) / (x^5 +x^2-1). Any significance? - G. Reed Jameson (Reedjameson(AT)yahoo.com), Dec 13 2007, Dec 16 2007

%F a(-n) = A136598(n).

%t LinearRecurrence[{0,1,0,0,1},{0,2,0,2,5},60] (* _Harvey P. Dale_, Oct 21 2015 *)

%o (PARI) {a(n) = if( n<0, n = 1 - n; polsym(x^5 + x^2 - 1, n)[n], n++; polsym(x^5 - x^3 - 1, n)[n])} /* _Michael Somos_, Feb 12 2012 */

%Y Cf. A007387, A001608, A135435, A136598.

%K easy,nonn

%O 1,2

%A G. Reed Jameson (Reedjameson(AT)yahoo.com), Nov 23 2007

%E More terms from _R. J. Mathar_, Nov 24 2007

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Last modified July 26 20:34 EDT 2021. Contains 346295 sequences. (Running on oeis4.)