cp's OEIS Frontend

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.

%I A074721 #39 Aug 21 2024 11:37:17
%S A074721 2,3,5,7,11,13,17,19,2,3,2,
%T A074721 93137414347535961677173798389971011031071091131,2,7,13,11,3,7,13,
%U A074721 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 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.
%C A074721 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 A074721 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 A074721 What is the next term after {2, 3, 5, 7, 11, 13, 17, 19}, if any, giving a(k)=A000040(k)?
%H A074721 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 A074721 Hans Havermann, <a href="http://chesswanks.com/seq/a074721.html">Two-color listing of 5359 terms</a>
%H A074721 Robert G. Wilson v, <a href="/A074721/a074721.txt">Table of n, a(n) for n = 1..1289</a>
%t A074721 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 A074721 (PARI)
%o A074721 a=0;
%o A074721 tryd(d) = { a=a*10+d; if(isprime(a),print(a);a=0); }
%o A074721 try(p) = { if(p>=10,try(p\10)); tryd(p%10); }
%o A074721 forprime(p=2,1000,try(p)); \\ _Jack Brennen_, Jun 25 2009
%o A074721 (Haskell)
%o A074721 a074721 n = a074721_list !! (n-1)
%o A074721 a074721_list = f 0 $ map toInteger a033308_list where
%o A074721    f c ds'@(d:ds) | a010051'' c == 1 = c : f 0 ds'
%o A074721                   | otherwise = f (10 * c + d) ds
%o A074721 -- _Reinhard Zumkeller_, Mar 11 2014
%Y A074721 Cf. A073034, A047777, A053648, A069090.
%Y A074721 Cf. A033308.
%K A074721 nonn,base,nice
%O A074721 1,1
%A A074721 _Reinhard Zumkeller_, Sep 04 2002
%E A074721 Edited by _Robert G. Wilson v_, Jun 26 2009
%E A074721 Further edited by _N. J. A. Sloane_, Jun 27 2009, incorporating comments from _Leroy Quet_, _Hans Havermann_, _Jack Brennen_ and _Franklin T. Adams-Watters_