The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133394 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A133394

a(n)=a(n-2)+a(n-5).
(history; published version)

#12 by Harvey P. Dale at Wed Oct 21 09:53:32 EDT 2015

STATUS

editing

approved

#11 by Harvey P. Dale at Wed Oct 21 09:53:21 EDT 2015

LINKS

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

STATUS

approved

editing

#10 by Harvey P. Dale at Wed Oct 21 09:52:11 EDT 2015

STATUS

editing

approved

#9 by Harvey P. Dale at Wed Oct 21 09:52:05 EDT 2015

LINKS

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

MATHEMATICA

LinearRecurrence[{0, 1, 0, 0, 1}, {0, 2, 0, 2, 5}, 60] (* Harvey P. Dale, Oct 21 2015 *)

STATUS

approved

editing

#8 by Charles R Greathouse IV at Wed Apr 30 01:33:23 EDT 2014

PROG

(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 */

Discussion

Wed Apr 30

01:33

OEIS Server: https://oeis.org/edit/global/2176

#7 by Russ Cox at Fri Mar 30 17:39:25 EDT 2012

COMMENTS

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 (mathar(AT)strw.leidenuniv.nl), _, Nov 24 2007

FORMULA

O.g.f.: -x*(2+5*x^3)/(-1+x^2+x^5). - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Nov 24 2007

EXTENSIONS

More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Nov 24 2007

Discussion

Fri Mar 30

17:39

OEIS Server: https://oeis.org/edit/global/190

#6 by T. D. Noe at Sun Feb 12 15:29:17 EST 2012

STATUS

proposed

approved

#5 by Michael Somos at Sun Feb 12 13:23:45 EST 2012

STATUS

editing

proposed

#4 by Michael Somos at Sun Feb 12 13:22:48 EST 2012

FORMULA

a(-n) = A136598(n).

PROG

(PARI) {a(n) = if( n<1, 0, n = 1 - n; polsym(x^5 + x^2 - 1, n)[n], n++; polsym(x^5 - x^3 - 1, n)[n])} /* Michael Somos Jan 11 2008 , Feb 12 2012 */

CROSSREFS

Cf. A007387, A001608, A135435, A136598.

STATUS

approved

editing

Discussion

Sun Feb 12

13:23

Michael Somos: Improved PARI function in relation to A136598. This is a  two-way infinite integer sequence.

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

COMMENTS

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 nth n-th term.

KEYWORD

easy,nonn,new