The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A267437 A linear recurrence related to the elliptic curves y^2 = x^3 -35*a^2*x - 98*a^3 with a = -1, -5, -6, -17, or -111. 3
 11, 23, 67, 151, 275, 487, 963, 2039, 4211, 8327, 16291, 32407, 65363, 131623, 263043, 524087, 1046579, 2095559, 4196707, 8394199, 16778003, 33544039, 67096899, 134226551, 268468211, 536886023, 1073691427, 2147403031, 4294987475, 8590116007, 17180010243 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Abatzoglou, Silverberg, Sutherland, & Wong give a quasi-quadratic algorithm for finding primes in this sequence, which relies on a correspondence between the Frobenius endomorphism of one of the five elliptic curves given above and complex multiplication in Z[(1 + sqrt(-7))/2]. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 2..3319 Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland, and Angela Wong, Deterministic elliptic curve primality proving for a special sequence of numbers, Tenth Algorithmic Number Theory Symposium (ANTS X, 2012), pp. 1-20. Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland, Angela Wong, Deterministic elliptic curve primality proving for a special sequence of numbers, arXiv:1202.3695 [math.NT], 2012. Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-4). FORMULA a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 4*a(n-4). a(n) ~ 4*2^n. G.f.: x^2*(11 - 21*x + 52*x^2 - 44*x^3)/((1 - x)*(1 - 2*x)*(1 - x + 2*x^2)). - Bruno Berselli, Jan 24 2016 a(n) = 1 + 2^(2+n) + 2*(1/2-(i*sqrt(7))/2)^n + 2*(1/2+(i*sqrt(7))/2)^n where i=sqrt(-1). - Colin Barker, Jul 02 2017 MATHEMATICA RecurrenceTable[{a[n] == 4 a[n - 1] - 7 a[n - 2] + 8 a[n - 3] - 4 a[n - 4], a[2] == 11, a[3] == 23, a[4] == 67, a[5] == 151}, a, {n, 2, 30}] (* Michael De Vlieger, Jan 24 2016 *) LinearRecurrence[{4, -7, 8, -4}, {11, 23, 67, 151}, 40] (* Vincenzo Librandi, Jan 27 2016 *) PROG (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 8, -7, 4]^n*[9; 11; 11; 23])[1, 1] (PARI) first(n)=if(n<5, return(first(5)[1..n-1])); my(v=vector(n-1)); v[1]=11; v[2]=23; v[3]=67; v[4]=151; for(k=5, #v, v[k]=4*v[k-1]-7*v[k-2]+8*v[k-3]-4*v[k-4]); v (Magma) I:=[11, 23, 67, 151]; [n le 4 select I[n] else 4*Self(n-1)-7*Self(n-2)+8*Self(n-3)-4*Self(n-4): n in [1..31]]; // Vincenzo Librandi, Jan 27 2016 (PARI) i=I; vector(50, n, n++; round(1 + 2^(2+n) + 2*(1/2-(i*sqrt(7))/2)^n + 2*(1/2+(i*sqrt(7))/2)^n)) \\ Colin Barker, Jul 02 2017 CROSSREFS Cf. A267438, A267439. Sequence in context: A081510 A068844 A139905 * A267438 A102273 A195463 Adjacent sequences: A267434 A267435 A267436 * A267438 A267439 A267440 KEYWORD nonn,easy AUTHOR Charles R Greathouse IV, Jan 15 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 01:03 EST 2022. Contains 358594 sequences. (Running on oeis4.)