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

11, 21, 32, 41, 53, 62, 74, 81, 95, 103, 116, 122, 137, 144, 158, 161, 179, 185, 191, 200, 213, 221, 231, 246, 251, 262, 272, 281, 293, 307, 311, 324, 334, 341, 355, 368, 371, 386, 391, 401, 417, 429, 431, 448, 455, 461, 479, 481, 492, 500, 510, 522, 531

Offset: 1

Author

Eric Angelini and Reinhard Zumkeller, Nov 20 2015

Keywords

• nonn
• base

Comments

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

Examples

			.   n |  1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10  | 11  | 12  | 13  | 14
. ----+----+---+---+---+---+---+---+---+---+-----+-----+-----+-----+-----
. a(n)| 11  21  32  41  53  62  74  81  95  103   116   122   137   144
. 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 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Éric Angelini, n concatenated with the nth digit of S, SeqFan list, Nov 19 2015.

Crossrefs

Cf. A003602.

Programs

Haskell

import Data.List (genericIndex)
a264646 n = a264646_list !! (n-1)
a264646_list = 11 : f 2 [0, 1, 1] where
   f x digs = (foldl (\v d -> 10 * v + d) 0 ys) : f (x + 1) (digs ++ ys)
     where ys = map (read . return) (show x) ++ [genericIndex digs x]

Python

from itertools import count, islice
def agen(): # generator of terms
    an, s = 11, [None, 1, 1]
    for n in count(2):
        yield an
        an = 10*n + s[n]
        s.extend(list(map(int, str(an))))
print(list(islice(agen(), 53))) # Michael S. Branicky, Oct 03 2024