A073062 -id:A073062 - cp's OEIS frontend

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

2, 23, 101, 4567, 67891, 789101, 4567891, 23456789, 728293031, 1234567891, 45678910111, 678910111213, 1222324252627, 12345678910111, 415161718192021, 3637383940414243, 12223242526272829, 910111213141516171

Offset: 1

Zak Seidov, Aug 22 2002

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

			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). - _Jonathan Vos Post_, Aug 25 2008

Robert Israel, Table of n, a(n) for n = 1..999
Eric W. Weisstein, Champernowne Constant. [From _Jonathan Vos Post_, Aug 25 2008]
Eric W. Weisstein, Copeland-Erdos Constant. [From _Jonathan Vos Post_, Aug 25 2008]

Cf. A003617. - M. F. Hasler, Aug 23 2008

Cf. A000040, A033307, A033308, A073062. - Jonathan Vos Post, Aug 25 2008

N:= 1000: # to use the concatenation of 1 to N
L:= NULL:
for n from 1 to N do
  L:= L, op(ListTools:-Reverse(convert(n,base,10)))
od:
L:= [L]:
nL:= nops(L);
f:= proc(n) local k,B,x;
  for k from 1 to nL-n+1 do
    B:= L[k..k+n-1];
    x:= add(B[i]*10^(n-i),i=1..n);
    if isprime(x) then return x fi
  od;
false;
end proc:
seq(f(n),n=1..100); # Robert Israel, Aug 16 2018

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}]

{s=Vec(Str(c=1)); for(d=1,30, for(j=1,9e9,
#sM. F. Hasler, Aug 23 2008

Edited by N. J. A. Sloane, Aug 19 2008 at the suggestion of R. J. Mathar

A073176 First n-digit prime in the concatenation of odd integers allowing leading zeros.

Original entry on oeis.org

3, 13, 911, 5791, 79111, 31051, 1232527, 23252729, 113151719, 2527293133, 57911131517, 991011031051, 6769717375777, 13579111315171, 135791113151719, 4547495153555759, 31517192123252729, 719212325272931333, 1131517192123252729, 71921232527293133353

Offset: 1

Zak Seidov, Aug 22 2002

Leading zeros count but are not printed (cf. A073428).

			a(4) = 5791 because first 4-digit prime in 135791113151719212325272931333537394143454749... is 5791. Notice that a(6) = 31051 because actually it is 031051, If we remove initial zeros, then a(6) = 105107.

Robert Israel, Table of n, a(n) for n = 1..996

Cf. A005408, A073062, A073175, A073428.

S:= "":
for i from 1 to 300 by 2 do
  S:= cat(S,sprintf("%d",i))
od:
nS:= length(S):
for n from 1 do
  found:= false;
  for i from 1 to nS-n+1 do
    x:= parse(S[i..n+i-1]);
    if isprime(x) then R[n]:= x; found:= true; break fi
  od;
  if not found then break fi;
od:
seq(R[i],i=1..n-1); # Robert Israel, Nov 27 2024

Data corrected by Sean A. Irvine, Nov 20 2024

Name modified by Sean A. Irvine, Jan 31 2025

cp's OEIS Frontend

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

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