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A181755 a(1) = 1, a(2) = 5. For n >= 3, a(n) is found by concatenating the first n-1 terms of the sequence and then dividing the resulting number by a(n-1). 9
1, 5, 3, 51, 301, 51001, 30100001, 5100100000001, 301000010000000000001, 5100100000001000000000000000000001, 3010000100000000000010000000000000000000000000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The calculations for the first few values of the sequence are

... a(3) = 15/5 = 3

... a(4) = 153/3 = 51

... a(5) = 15351/51 = 301

... a(6) = 15351301/301 = 51001.

For similarly defined sequences see A181754, A184756 and A181864 through A181870.

LINKS

Table of n, a(n) for n=1..11.

FORMULA

DEFINITION

a(1) = 1, a(2) = 5, and for n >= 3

(1)... a(n) = concatenate(a(1),a(2),...,a(n-1))/a(n-1).

RECURRENCE RELATION

For n >= 2

(2)... a(n+2) = 10^F(n)*a(n)+1,

where F(n) = A000045(n) are the Fibonacci numbers.

For n >= 2, a(n) has F(n-1) digits.

MAPLE

#A181755

M:=11:

a:=array(1..M):s:=array(1..M):

a[1]:=1:a[2]:=5:

s[1]:=convert(a[1], string):

s[2]:=cat(s[1], convert(a[2], string)):

for n from 3 to M do

a[n] := parse(s[n-1])/a[n-1];

s[n]:= cat(s[n-1], convert(a[n], string));

end do:

seq(a[n], n = 1..M);

MATHEMATICA

nxt[lst_]:=Module[{nt=FromDigits[Flatten[IntegerDigits/@lst]]/Last[ lst]}, Flatten[{lst, nt}]]; Nest[nxt[#]&, {1, 5}, 10] (* Harvey P. Dale, Aug 08 2014 *)

CROSSREFS

Cf. A000045, A181754, A181756, A181864, A181865, A181866, A181867, A181868, A181869, A181870

Sequence in context: A323779 A343290 A027858 * A007299 A257935 A109254

Adjacent sequences:  A181752 A181753 A181754 * A181756 A181757 A181758

KEYWORD

easy,nonn,base

AUTHOR

Peter Bala, Nov 09 2010

STATUS

approved

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)