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Search: id:A074721
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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; listen)
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OFFSET
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1,1
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COMMENT
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Problem: what is the sequence giving the least k with a(k)=A000040(k)?
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.
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LINKS
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Robert G. Wilson v, (rgwv(AT)rgwv.com), 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)
Robert G. Wilson v, (rgwv(AT)rgwv.com), Table of n, a(n) for n = 1..1289 .
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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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PROGRAM
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(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
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Cf. A073034, A047777, A053648, A069090.
Sequence in context: A117285 A100546 A117094 this_sequence A152073 A117289 A106317
Adjacent sequences: A074718 A074719 A074720 this_sequence A074722 A074723 A074724
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KEYWORD
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nonn,base,nice
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 04 2002
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EXTENSIONS
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a(1290) exceeds 11860 digits and begins with the digits 4203 followed by the primes beginning with the 2695th prime 24223, etc. - Robert G. Wilson v, Jun 26 2009
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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