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A073175 First occurrence of an n-digit prime as a substring in the concatenation of the natural numbers 12345678910111213141516171819202122232425262728293031.... 4

%I

%S 2,23,101,4567,67891,789101,4567891,23456789,728293031,1234567891,

%T 45678910111,678910111213,1222324252627,12345678910111,

%U 415161718192021,3637383940414243,12223242526272829,910111213141516171

%N First occurrence of an n-digit prime as a substring in the concatenation of the natural numbers 12345678910111213141516171819202122232425262728293031....

%C This is to Champernowne's constant 0.12345678910111213... (Sloane's A033307) as A073062 is to A033308 Decimal expansion of Copeland-Erdos constant: concatenate primes. - _Jonathan Vos Post_, Aug 25 2008

%H Robert Israel, <a href="/A073175/b073175.txt">Table of n, a(n) for n = 1..999</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/ChampernowneConstant.html">Champernowne Constant.</a> [From _Jonathan Vos Post_, Aug 25 2008]

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Copeland-ErdosConstant.html">Copeland-Erdos Constant.</a> [From _Jonathan Vos Post_, Aug 25 2008]

%e Take 1234567891011121314151617....; a(4)=4567 because the first 4-digit prime in the sequence is 4567.

%e 1213 is < 4567 but occurs later in the string.

%e a(5) = 67891 is the first occurrence of a five-digit substring that is a prime, 12345(67891)011121314...

%e 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). - _Jonathan Vos Post_, Aug 25 2008

%p N:= 1000: # to use the concatenation of 1 to N

%p L:= NULL:

%p for n from 1 to N do

%p L:= L, op(ListTools:-Reverse(convert(n,base,10)))

%p od:

%p L:= [L]:

%p nL:= nops(L);

%p f:= proc(n) local k,B,x;

%p for k from 1 to nL-n+1 do

%p B:= L[k..k+n-1];

%p x:= add(B[i]*10^(n-i),i=1..n);

%p if isprime(x) then return x fi

%p od;

%p false;

%p end proc:

%p seq(f(n),n=1..100); # _Robert Israel_, Aug 16 2018

%t 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}]

%o (PARI) {s=Vec(Str(c=1)); for(d=1,30, for(j=1,9e9,

%o #s<d+j && s=concat( s,Vec( Str( c++ ))); s[j]=="0" && next;

%o isprime( p=eval( concat( vecextract( s,Str(j,"..",j+d-1) )))) || next;

%o print(d," ",p); next(2)))} /* replace "isprime" by 2==bigomega to get the semiprime analog */ \\ _M. F. Hasler_, Aug 23 2008

%Y Cf. A003617. - _M. F. Hasler_, Aug 23 2008

%Y Cf. A000040, A033307, A033308, A073062. - _Jonathan Vos Post_, Aug 25 2008

%K base,nonn

%O 1,1

%A _Zak Seidov_, Aug 22 2002

%E Edited by _N. J. A. Sloane_, Aug 19 2008 at the suggestion of _R. J. Mathar_

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)