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.

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

Author

Reinhard Zumkeller, Sep 04 2002

Keywords

• nonn
• base
• nice

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]
• Hans Havermann, Two-color listing of 5359 terms
• Robert G. Wilson v, Table of n, a(n) for n = 1..1289

Crossrefs

Cf. A073034, A047777, A053648, A069090.

Cf. A033308.

Programs

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

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}]

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

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