[go: up one dir, main page]

login
A074721
Concatenate the primes as 2357111317192329313..., then insert commas from left to right so that between each pair of successive commas is a prime, always making the new prime as small as possible.
5
2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 2, 93137414347535961677173798389971011031071091131, 2, 7, 13, 11, 3, 7, 13, 91491511, 5, 7, 163, 167, 17, 3, 17, 9181, 19, 11, 9319, 7, 19, 9211223227229233239241251257, 2, 6326927, 127, 7, 2, 81283, 2, 93307, 3, 11, 3, 13, 3, 17, 3, 3, 13, 3, 7, 3, 47, 3, 493533593673733
OFFSET
1,1
COMMENTS
Note that leading zeros are dropped. Example: When the primes 691, 701, 709, and 719 get concatenated and digitized, they become {..., 6, 9, 1, 7, 0, 1, 7, 0, 9, 7, 1, 9, ...}. These will end up in A074721 as: a(98)=691, a(99)=7, a(100)=17, a(101)=97, a(102)=19, ..., . Terms a(100) & a(101) have associated with them unstated leading zeros. - Hans Havermann, Jun 26 2009
Large terms in the links are probable primes only. For example, a(1290) has 24744 digits and a(4050), 32676 digits. If of course any probable primes were not actual primes, the indexing of subsequent terms would be altered. - Hans Havermann, Dec 28 2010
What is the next term after {2, 3, 5, 7, 11, 13, 17, 19}, if any, giving a(k)=A000040(k)?
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..329 [a(330) is too large to be included in a b-file: see the a-file]
MATHEMATICA
id = IntegerDigits@ Array[ Prime, 3000] // Flatten; lst = {}; Do[ k = 1; While[ p = FromDigits@ Take[ id, k]; !PrimeQ@p || p == 1, k++ ]; AppendTo[lst, p]; id = Drop[id, k], {n, 1289}]
PROG
(PARI)
a=0;
tryd(d) = { a=a*10+d; if(isprime(a), print(a); a=0); }
try(p) = { if(p>=10, try(p\10)); tryd(p%10); }
forprime(p=2, 1000, try(p)); \\ Jack Brennen, Jun 25 2009
(Haskell)
a074721 n = a074721_list !! (n-1)
a074721_list = f 0 $ map toInteger a033308_list where
f c ds'@(d:ds) | a010051'' c == 1 = c : f 0 ds'
| otherwise = f (10 * c + d) ds
-- Reinhard Zumkeller, Mar 11 2014
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
Reinhard Zumkeller, Sep 04 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jun 26 2009
Further edited by N. J. A. Sloane, Jun 27 2009, incorporating comments from Leroy Quet, Hans Havermann, Jack Brennen and Franklin T. Adams-Watters
STATUS
approved