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A262282 a(1)=11. For n>1, let s denote the digit-string of a(n-1) with the first digit omitted. Then a(n) is the smallest prime not yet present which starts with s. 4
11, 13, 3, 2, 5, 7, 17, 71, 19, 97, 73, 31, 101, 103, 37, 79, 907, 701, 107, 709, 911, 113, 131, 311, 1103, 1031, 313, 137, 373, 733, 331, 317, 173, 739, 397, 971, 719, 191, 919, 193, 937, 379, 797, 977, 773, 7307, 307, 727, 271, 7103, 1033, 337, 3701, 7013 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If a(n-1) has a single digit then a(n) is simply the smallest missing prime.
Leading zeros in s are ignored.
The b-file suggests that there are infinitely many primes that do not appear in the sequence. However, there is no proof at present that any particular prime (23, say) never appears.
Alois P. Heinz points out that this sequence and A262283 eventually merge (see the latter entry for details). - N. J. A. Sloane, Sep 19 2015
A variant without the prime number condition: A262356. - Reinhard Zumkeller, Sep 19 2015
LINKS
EXAMPLE
a(1)=11, so s=1, a(2) is smallest missing prime that starts with 1, so a(2)=13. Then s=3, so a(3)=3. Then s is the empty string, so a(4)=2, and so on.
PROG
(Haskell)
import Data.List (isPrefixOf, delete)
a262282 n = a262282_list !! (n-1)
a262282_list = 11 : f "1" (map show (delete 11 a000040_list)) where
f xs pss = (read ys :: Integer) :
f (dropWhile (== '0') ys') (delete ys pss)
where ys@(_:ys') = head $ filter (isPrefixOf xs) pss
-- Reinhard Zumkeller, Sep 19 2015
CROSSREFS
Suggested by A089755. Cf. A262283.
Cf. A262356.
Sequence in context: A022481 A156338 A272817 * A034080 A107805 A177378
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Sep 18 2015
STATUS
approved

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Last modified April 25 11:16 EDT 2024. Contains 371967 sequences. (Running on oeis4.)