A074721 - OEIS

%I #39 Aug 21 2024 11:37:17

%S 2,3,5,7,11,13,17,19,2,3,2,

%T 93137414347535961677173798389971011031071091131,2,7,13,11,3,7,13,

%U 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

%N 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.

%C 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

%C 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

%C What is the next term after {2, 3, 5, 7, 11, 13, 17, 19}, if any, giving a(k)=A000040(k)?

%H Robert G. Wilson v, <a href="/A074721/b074721.txt">Table of n, a(n) for n = 1..329</a> [a(330) is too large to be included in a b-file: see the a-file]

%H Hans Havermann, <a href="http://chesswanks.com/seq/a074721.html">Two-color listing of 5359 terms</a>

%H Robert G. Wilson v, <a href="/A074721/a074721.txt">Table of n, a(n) for n = 1..1289</a>

%t 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}]

%o (PARI)

%o a=0;

%o tryd(d) = { a=a*10+d; if(isprime(a),print(a);a=0); }

%o try(p) = { if(p>=10,try(p\10)); tryd(p%10); }

%o forprime(p=2,1000,try(p)); \\ _Jack Brennen_, Jun 25 2009

%o (Haskell)

%o a074721 n = a074721_list !! (n-1)

%o a074721_list = f 0 $ map toInteger a033308_list where

%o    f c ds'@(d:ds) | a010051'' c == 1 = c : f 0 ds'

%o                   | otherwise = f (10 * c + d) ds

%o -- _Reinhard Zumkeller_, Mar 11 2014

%Y Cf. A073034, A047777, A053648, A069090.

%Y Cf. A033308.

%K nonn,base,nice

%O 1,1

%A _Reinhard Zumkeller_, Sep 04 2002

%E Edited by _Robert G. Wilson v_, Jun 26 2009

%E Further edited by _N. J. A. Sloane_, Jun 27 2009, incorporating comments from _Leroy Quet_, _Hans Havermann_, _Jack Brennen_ and _Franklin T. Adams-Watters_