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A074721
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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.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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)?
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LINKS
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MATHEMATICA
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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
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(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); }
(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
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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