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

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, 249, 306, 387, 464, 592, 713, 898, 1100, 1362, 1692, 2075, 2590, 3175, 3952, 4867, 6027, 7457, 9202, 11409, 14069, 17436, 21526, 26638, 32935, 40707, 50371, 62233

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

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.

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1).

Crossrefs

Cf. A007387, A001608, A135435, A136598.

Programs

Mathematica

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

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 */

Formula

O.g.f.: -x*(2+5*x^3)/(-1+x^2+x^5). - R. J. Mathar, Nov 24 2007

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

a(-n) = A136598(n).

Extensions

More terms from R. J. Mathar, Nov 24 2007