A174840 Least k such that the primes 3 to prime(k+1) form a complete residue system (mod prime(n)).

3, 7, 9, 13, 26, 26, 42, 32, 65, 63, 84, 74, 89, 162, 110, 126, 177, 169, 144, 171, 214, 196, 237, 238, 323, 297, 363, 344, 327, 515, 441, 543, 420, 481, 612, 494, 604, 543, 646, 552, 645, 644, 519, 742, 593, 737, 644, 851, 1012, 787, 1204, 727, 899, 800, 1046

Offset: 1

Author

Keith Backman, Mar 30 2010

Keywords

• nonn

Comments

If the value of the terminal prime is given rather than its index in the list of odd primes, the sequence becomes 7 19 29 43 103 103 191 137 347 311 439

In other words, the odd primes no larger than 7 form a complete residue set mod 3, the odd primes no larger than 19 form a complete residue set mod 5, and so forth

Programs

Mathematica

Table[p=Prime[n]; k=1; While[u=Union[Mod[Prime[Range[2,k]], p]]; u != Range[0,p-1], k++ ]; k-1, {n,2,100}] (* T. D. Noe, Apr 02 2010 *)

Extensions

Name improved by T. D. Noe, Apr 05 2010

Corrected and extended by T. D. Noe, Apr 02 2010