A037487 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2.

1, 12, 121, 1212, 12121, 121212, 1212121, 12121212, 121212121, 1212121212, 12121212121, 121212121212, 1212121212121, 12121212121212, 121212121212121, 1212121212121212, 12121212121212121, 121212121212121212, 1212121212121212121, 12121212121212121212

Offset

1,2

Comments

See A037610 for a general formula. - Hieronymus Fischer, Jan 03 2013

(Smoothly undulating palindromic) primes in this sequence are listed in A092696(n) = (4*10^A062209(n)-7)/33. - M. F. Hasler, Jul 30 2015

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

Formula

a(n) = floor((4/33)*10^n). - Hieronymus Fischer, Jan 03 2013

a(n) = 10*a(n-1)+a(n-2)-10*a(n-3). G.f.: x*(2*x+1) / ((x-1)*(x+1)*(10*x-1)). - Colin Barker, Apr 30 2014

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 2}]], {n, 20}] (* or *) LinearRecurrence[ {10, 1, -10}, {1, 12, 121}, 20] (* Harvey P. Dale, Jun 21 2016 *)

Prog

(PARI) A037487(n)=10^n*4\33  \\ - M. F. Hasler, Jan 13 2013
(PARI) Vec(x*(2*x+1)/((x-1)*(x+1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Apr 30 2014

Crossrefs

Cf. A037610.

Sequence in context: A098297 A037543 A214317 * A332603 A358615 A231869

Adjacent sequences: A037484 A037485 A037486 * A037488 A037489 A037490

Keyword

nonn,base

Author

Clark Kimberling

Status

approved