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A262283 a(1)=2. 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. 6
2, 3, 5, 7, 11, 13, 31, 17, 71, 19, 97, 73, 37, 79, 907, 701, 101, 103, 307, 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, 3079, 7901, 9011, 1109, 109, 929, 29, 941, 41 (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 sequence is infinite, since there infinitely many primes that start with s (see the comments in A080165).

The data in the b-file suggests that there are infinitely many primes that do not appear. Hoever, at present that is no proof that even one prime (23, say) never appears. - N. J. A. Sloane, Sep 20 2015

Alois P. Heinz points out that a(n) = A262282(n+29) starting at the 103rd term. - N. J. A. Sloane, Sep 19 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..676

EXAMPLE

a(1)=2, so s is the empty string, so a(2) is the smallest missing prime, 3. After a(6)=13, s=3, so a(7) is the smallest missing prime that starts with 3, which is 31.

PROG

(Haskell)

import Data.List (isPrefixOf, delete)

a262283 n = a262283_list !! (n-1)

a262283_list = 2 : f "" (map show $ tail 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

Cf. A080165, A089755, A262282, A262350.

Sequence in context: A162567 A067908 A236128 * A187614 A191077 A262377

Adjacent sequences:  A262280 A262281 A262282 * A262284 A262285 A262286

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Sep 18 2015

EXTENSIONS

More terms from Alois P. Heinz, Sep 18 2015

STATUS

approved

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Last modified October 16 13:21 EDT 2019. Contains 328083 sequences. (Running on oeis4.)