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A073175
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First occurrence of an n-digit prime as a substring in the concatenation of the natural numbers 12345678910111213141516171819202122232425262728293031....
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3
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2, 23, 101, 4567, 67891, 789101, 4567891, 23456789, 728293031, 1234567891, 45678910111, 678910111213, 1222324252627, 12345678910111, 415161718192021, 3637383940414243, 12223242526272829, 910111213141516171
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is to Champernowne's constant 0.12345678910111213... (Sloane's A033307) as A073062 is to A033308 Decimal expansion of Copeland-Erdos constant: concatenate primes. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2008]
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LINKS
| Eric W. Weisstein, Champernowne Constant. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2008]
Eric W. Weisstein, Copeland-Erdos Constant. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2008]
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EXAMPLE
| Take 1234567891011121314151617....; a(4)=4567 because the first 4-digit prime in the sequence is 4567.
1213 is < 4567 but occurs later in the string.
a(5) = 67891 is the first occurrence of a five-digit substring that is a prime, 12345(67891)011121314...
a(1) = 2 = prime(1). a(2) = 23 = prime(9). a(3) = 571 = prime(105). a(4) = 2357 = prime(350). a(5) = 11131 = prime(1349). [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2008]
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MATHEMATICA
| p200=Flatten[IntegerDigits[Range[200]]]; Do[pn=Partition[p200, n, 1]; ln=Length[pn]; tab=Table[Sum[10^(n-k)*pn[[i, k]], {k, n}], {i, ln}]; Print[{n, Select[tab, PrimeQ][[1]]}], {n, 20}]
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PROG
| Contribution from M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 23 2008: (Start)
(PARI) {s=Vec(Str(c=1)); for(d=1, 30, for(j=1, 9e9,
#s<d+j && s=concat( s, Vec( Str( c++ ))); s[j]=="0" && next;
isprime( p=eval( concat( vecextract( s, Str(j, "..", j+d-1) )))) || next;
print(d, " ", p); next(2)))} /* replace "isprime" by 2==bigomega to get the semiprime analogue */ (End)
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CROSSREFS
| Cf. A003617 [From M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 23 2008]
Cf. A000040, A033307, A033308, A073062. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2008]
Sequence in context: A131176 A141405 A068876 * A141888 A201851 A034523
Adjacent sequences: A073172 A073173 A073174 * A073176 A073177 A073178
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KEYWORD
| base,nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Aug 22 2002
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 19 2008 at the suggestion of R. J. Mathar
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