A187930 Least number r such that r == k-1 (mod prime(k)) for k = 1..n.

0, 4, 22, 52, 1522, 29242, 299512, 4383592, 188677702, 5765999452, 5765999452, 2211931390882, 165468170356702, 8075975022064162, 361310530977154972, 20037783573808880092, 1779852341342071295512, 40235059344426324076912, 4966347076439519105374252, 169991099649125127278835142

Offset: 1

Author

Michel Lagneau, Mar 16 2011

Keywords

• nonn

Examples

			a(4) = 1522 because :
1522 == 0 (mod 2) ;
1522 == 1 (mod 3);
1522 == 2 (mod 5);
1522 == 3 (mod 7);
1522 == 4 (mod 11).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A070198.

Programs

Maple

with(numtheory):nn:=100:T:=array(1..nn):pr:=1:for k from 1 to nn do: pr:=pr*ithprime(k):T[k]:=pr:od:for  m from 1 to nn do:z:=T[m]:pp:=ithprime(m):id:=0:for x from 0 to z-1 while (id=0)  do:it:=0:for y from 0 to m-1 do:r:=ithprime(y+1):a:=irem(x,r):if a=y then it:=it+1:else
  fi: od:if it =m then id:=1:print(x):else fi:od:od:

Mathematica

Table[ChineseRemainder[Range[n] - 1, Prime[Range[n]]], {n, 20}]

Formula

a(n) = A053664(n) - 1.