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A047855 a(n) = T(7, n), array T given by A047848. 16
1, 2, 12, 112, 1112, 11112, 111112, 1111112, 11111112, 111111112, 1111111112, 11111111112, 111111111112, 1111111111112, 11111111111112, 111111111111112, 1111111111111112, 11111111111111112, 111111111111111112, 1111111111111111112, 11111111111111111112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Range of A164898, apart from first term. - Reinhard Zumkeller, Aug 30 2009

a(n) is the number of integers less than or equal to 10^n, whose initial digit is 1. - Michel Marcus, Jul 04 2019

a(n) is 2^n represented in bijective base-2 numeration. - Alois P. Heinz, Aug 26 2019

This sequence proves both A028842 (numbers with prime product of digits) and A028843 (numbers with prime iterated product of digits) are infinite. Proof: Suppose either of those sequences is finite. Label as omega the supposed last term. Compute n = ceiling(log_10 omega) + 1. Then a(n) > omega. The product of digits of a(n) is 2, contradicting the assumption that omega is the final term of either A028842 or A028843. - Alonso del Arte, Apr 14 2020

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..200

Wikipedia, Bijective numeration

FORMULA

a(n) = (10^n + 8)/9. - Ralf Stephan, Feb 14 2004

a(0) = 1, a(1) = 2, a(n) = 11*a(n - 1) - 10*a(n - 2) for n > 1. - Lambert Klasen (lambert.klasen(AT)gmx.net), Jan 28 2005

G.f.: (1 - 9*x)/(1 - 11*x + 10*x^2). - Philippe Deléham, Oct 05 2009

a(n) = 10*a(n-1) - 8 (with a(0) = 1). - Vincenzo Librandi, Aug 06 2010

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=10*a[n-1]+1 od: seq(a[n]+1, n=0..18); # Zerinvary Lajos, Mar 20 2008

MATHEMATICA

Join[{1}, Table[FromDigits[PadLeft[{2}, n, 1]], {n, 30}]] (* Harvey P. Dale, Apr 17 2013 *)

(10^Range[0, 29] + 8)/9 (* Alonso del Arte, Apr 12 2020 *)

PROG

(PARI) a(n)=if(n==0, 1, if(n==1, 2, 11*a(n-1)-10*a(n-2)))

for(i=0, 10, print1(a(i), ", ")) \\ Lambert Klasen, Jan 28 2005

(Sage) [gaussian_binomial(n, 1, 10)+1 for n in range(17)] # Zerinvary Lajos, May 29 2009

(Scala) (List.fill(20)(10: BigInt)).scanLeft(1: BigInt)(_ * _).map(n => (n + 8)/9) // Alonso del Arte, Apr 12 2020

CROSSREFS

n-th difference of a(n), a(n-1), ..., a(0) is 9^(n-1) for n = 1, 2, 3, ...

Sequence in context: A102659 A212659 A191895 * A199045 A009232 A218222

Adjacent sequences:  A047852 A047853 A047854 * A047856 A047857 A047858

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Harvey P. Dale, Apr 17 2013

STATUS

approved

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Last modified September 26 02:39 EDT 2020. Contains 337346 sequences. (Running on oeis4.)