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A074721
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Take A000040, omit commas: 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.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 the next term after {2, 3, 5, 7, 11, 13, 17, 19}, if any, giving a(k)=A000040(k)?
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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
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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}]
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PROG
| (PARI, from Jack Brennen, Jun 25 2009)
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));
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CROSSREFS
| Cf. A073034, A047777, A053648, A069090.
Sequence in context: A100546 A117094 A171057 * A152073 A117289 A106317
Adjacent sequences: A074718 A074719 A074720 * A074722 A074723 A074724
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KEYWORD
| nonn,base,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 04 2002
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EXTENSIONS
| Edited by Robert G. Wilson, v (rgwv(AT)rgwv.com), 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.
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