A105581 -id:A105581 - cp's OEIS frontend

A105580 a(n+3) = a(n) - a(n+1) - a(n+2); a(0) = -5, a(1) = 6, a(2) = 0.

-5, 6, 0, -11, 17, -6, -22, 45, -29, -38, 112, -103, -47, 262, -318, 9, 571, -898, 336, 1133, -2367, 1570, 1930, -5867, 5507, 2290, -13664, 16881, -927, -29618, 47426, -18735, -58309, 124470, -84896, -97883, 307249, -294262, -110870, 712381, -895773, 72522, 1535632, -2503927, 1040817, 2998742

Offset: 0

Creighton Dement, Apr 14 2005

Floretion Algebra Multiplication Program, FAMP Code: 2tesforseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e], 1vesforseq = A000004, ForType: 1A.

			This sequence was generated using the same floretion which generated the sequences A105577, A105578, A105579, etc.. However, in this case a force transform was applied. [Specifically, (a(n)) may be seen as the result of a tesfor-transform of the zero-sequence A000004 with respect to the floretion given in the program code.]

Index entries for linear recurrences with constant coefficients, signature (-1,-1,1).

Cf. A002249, A014551, A078020, A105577, A105578, A105581.

Transpose[NestList[Join[Rest[#],ListCorrelate[ {1,-1,-1}, #]]&,{-5,6,0},50]][[1]]  (* Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[(5-x-x^2)/(x^3-x^2-x-1),{x,0,50}],x]  (* Harvey P. Dale, Mar 14 2011 *)

G.f. (5-x-x^2)/(x^3-x^2-x-1)
a(n) = A078046(n-1) - A073145(n+3).
a(n) = -5*A057597(n+2) + A057597(n+1)+A057597(n). - R. J. Mathar, Oct 25 2022

A258433 Primes with repdigit indices (in decimal).

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 79, 137, 193, 257, 317, 389, 457, 523, 607, 1399, 2239, 3119, 4019, 4973, 5903, 6907, 7907, 8933, 19583, 30911, 42473, 54581, 66889, 79357, 92003, 104723, 117763, 252233, 393191, 538259, 686671, 836833, 989999, 1144153, 1299689, 1456667, 3080969, 4767181, 6495109, 8251153

Offset: 1

James G. Merickel, May 29 2015

Elements of this sequence are the first 9 primes, then the 11th, 22nd, 33rd, ... , 99th, 111th, 222nd, etc. This is a somewhat remarkable sequence because of certain digital coincidences (see Prime Curios links).

			The first prime skipped is the 10th, 29, so that a(10)=31.  Then follows a(11)=79, a(12)=137, a(13)=193, etc.: The 22nd, 33rd, and 44th primes, and so on.

Charles R Greathouse IV, Table of n, a(n) for n = 1..153
Andrew Booker, The Nth Prime Page
Prime Curios!, 989999
Prime Curios!, 640663963
Wikipedia, Repdigit
Wikipedia, Prime-counting function

Cf. A000040, A010785, A105581.

Prime[#]&/@(FromDigits/@Flatten[Table[PadRight[{},k,n],{k,6},{n,9}],1]) (* Harvey P. Dale, Mar 25 2019 *)

a(n)=prime(10^((n+8)\9)\9*((n-1)%9+1)) \\ Charles R Greathouse IV, Jun 03 2015

a(n) = A000040(A010785(n)).

cp's OEIS Frontend

A105580 a(n+3) = a(n) - a(n+1) - a(n+2); a(0) = -5, a(1) = 6, a(2) = 0.

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