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A264646 A simple self-describing sequence S: n concatenated with the n-th digit of S.

%I A264646 #19 Dec 23 2024 14:53:44
%S A264646 11,21,32,41,53,62,74,81,95,103,116,122,137,144,158,161,179,185,191,
%T A264646 200,213,221,231,246,251,262,272,281,293,307,311,324,334,341,355,368,
%U A264646 371,386,391,401,417,429,431,448,455,461,479,481,492,500,510,522,531
%N A264646 A simple self-describing sequence S: n concatenated with the n-th digit of S.
%C A264646 Although A003602 and this sequence initially agree in their digit-streams, they differ after 48 digits. - _N. J. A. Sloane_, Nov 20 2015
%H A264646 Reinhard Zumkeller, <a href="/A264646/b264646.txt">Table of n, a(n) for n = 1..10000</a>
%H A264646 Éric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-November/015661.html">n concatenated with the nth digit of S</a>, SeqFan list, Nov 19 2015.
%e A264646 .   n |  1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10  | 11  | 12  | 13  | 14
%e A264646 . ----+----+---+---+---+---+---+---+---+---+-----+-----+-----+-----+-----
%e A264646 . a(n)| 11  21  32  41  53  62  74  81  95  103   116   122   137   144
%e A264646 . digs| 1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1 9 5 1 0 3 1 1 6 1 2 2 1 3 7 1 4 4 .
%o A264646 (Haskell)
%o A264646 import Data.List (genericIndex)
%o A264646 a264646 n = a264646_list !! (n-1)
%o A264646 a264646_list = 11 : f 2 [0, 1, 1] where
%o A264646    f x digs = (foldl (\v d -> 10 * v + d) 0 ys) : f (x + 1) (digs ++ ys)
%o A264646      where ys = map (read . return) (show x) ++ [genericIndex digs x]
%o A264646 (Python)
%o A264646 from itertools import count, islice
%o A264646 def agen(): # generator of terms
%o A264646     an, s = 11, [None, 1, 1]
%o A264646     for n in count(2):
%o A264646         yield an
%o A264646         an = 10*n + s[n]
%o A264646         s.extend(list(map(int, str(an))))
%o A264646 print(list(islice(agen(), 53))) # _Michael S. Branicky_, Oct 03 2024
%Y A264646 Cf. A003602.
%K A264646 nonn,base
%O A264646 1,1
%A A264646 _Eric Angelini_ and _Reinhard Zumkeller_, Nov 20 2015