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A074721 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. +0
3
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)
OFFSET

1,1

COMMENT

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.

LINKS

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 .

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}]

PROGRAM

(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));

CROSSREFS

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

KEYWORD

nonn,base,nice

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 04 2002

EXTENSIONS

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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Last modified November 29 12:46 EST 2009. Contains 167659 sequences.


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