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 A181754 a(1) = 1, a(2) = 2. 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). 10
 1, 2, 6, 21, 601, 21001, 60100001, 2100100000001, 601000010000000000001, 2100100000001000000000000000000001, 6010000100000000000010000000000000000000000000000000001 (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) = 12/2 = 6 ... a(4) = 126/6 = 21 ... a(5) = 12621/21 = 601 ... a(6) = 12621601/601 = 21001. Similar sequences may be formed by 1) starting with different initial values. See A181755 and A181756. 2) concatenating the k-th powers of the first n-1 terms of the sequence before dividing by a(n-1). See A181864, A181865 and A181866. 3) concatenating the k-th powers of the first n-1 terms of the sequence in reverse order before dividing by a(n-1). See A181867, A181868, A181869 and A181870. LINKS FORMULA DEFINITION a(1) = 1, a(2) = 2, 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 M:=11: a:=array(1..M):s:=array(1..M): a:=1:a:=2: s:=convert(a, string): s:=cat(s, convert(a, 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); CROSSREFS Cf. A000045, A181755, A181756, A181864, A181865, A181866, A181867, A181868, A181869, A181870 Sequence in context: A110306 A028936 A066932 * A084392 A156155 A263486 Adjacent sequences:  A181751 A181752 A181753 * A181755 A181756 A181757 KEYWORD easy,nonn,base AUTHOR Peter Bala, Nov 09 2010 STATUS approved

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)