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A simple self-describing sequence S: n concatenated with the n-th digit of S.
6

%I #18 Oct 04 2024 06:54:25

%S 11,21,32,41,53,62,74,81,95,103,116,122,137,144,158,161,179,185,191,

%T 200,213,221,231,246,251,262,272,281,293,307,311,324,334,341,355,368,

%U 371,386,391,401,417,429,431,448,455,461,479,481,492,500,510,522,531

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

%C Although A003602 and this sequence initially agree in their digit-streams, they differ after 48 digits. - _N. J. A. Sloane_, Nov 20 2015

%H Reinhard Zumkeller, <a href="/A264646/b264646.txt">Table of n, a(n) for n = 1..10000</a>

%H Éric Angelini, <a href="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 . n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14

%e . ----+----+---+---+---+---+---+---+---+---+-----+-----+-----+-----+-----

%e . a(n)| 11 21 32 41 53 62 74 81 95 103 116 122 137 144

%e . 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 (Haskell)

%o import Data.List (genericIndex)

%o a264646 n = a264646_list !! (n-1)

%o a264646_list = 11 : f 2 [0, 1, 1] where

%o f x digs = (foldl (\v d -> 10 * v + d) 0 ys) : f (x + 1) (digs ++ ys)

%o where ys = map (read . return) (show x) ++ [genericIndex digs x]

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o an, s = 11, [None, 1, 1]

%o for n in count(2):

%o yield an

%o an = 10*n + s[n]

%o s.extend(list(map(int, str(an))))

%o print(list(islice(agen(), 53))) # _Michael S. Branicky_, Oct 03 2024

%Y Cf. A003602.

%K nonn,base

%O 1,1

%A _Eric Angelini_ and _Reinhard Zumkeller_, Nov 20 2015