A072921 a(1)=1; a(n) = a(n-1) + [sum of all decimal digits present so far in the sequence].
1, 2, 5, 13, 25, 44, 71, 106, 148, 203, 263, 334, 415, 506, 608, 724, 853, 998, 1169, 1357, 1561, 1778, 2018, 2269, 2539, 2828, 3137, 3460, 3796, 4157, 4535, 4930, 5341, 5765, 6212, 6670, 7147, 7643, 8159, 8698, 9268, 9863, 10484, 11122
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
-
Maple
b:= proc(n) option remember; local m; m:= a(n); `if`(n=1, 0, b(n-1)); while m>0 do %+ irem(m, 10, 'm') od; % end: a:= proc(n) option remember; `if`(n=1, 1, a(n-1) +b(n-1)) end: seq(a(n), n=1..50); # Alois P. Heinz, Jun 01 2010 -
Mathematica
a[1]=1;a[2]=2;a[n_]:=a[n]=2*a[n-1]-a[n-2]+Apply[Plus,IntegerDigits[a[n-1]]];Table[a[n],{n,100}] (* Farideh Firoozbakht, Oct 01 2009 *) a[1] = 1; a[n_] := a[n] = a[n - 1] + Plus @@ Flatten[ Map[ IntegerDigits, Array[a, n - 1]]]; Array[a, 100] (* Robert G. Wilson v, Oct 01 2009 *) -
Python
from itertools import islice def agen(): # generator of terms an, anp1 = 1, 2 while True: yield an an, anp1 = anp1, 2*anp1 - an + sum(map(int, str(anp1))) print(list(islice(agen(), 44))) # Michael S. Branicky, Oct 01 2024
Formula
a(1)=1, a(2)=2; a(n+1)=2a(n)-a(n-1)+sod(a(n)) (sod = "sum of digits"). - Farideh Firoozbakht, Oct 01 2009
Asymptotically it seems a(n)~c*n^2*log(n) for c~1.99... - Benoit Cloitre, Oct 07 2009
Extensions
More terms from Alois P. Heinz, Oct 01 2009
Comments