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

2,1

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

Links

Robert Israel, Table of n, a(n) for n = 2..5000

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
f:= proc(n) local S, k;
  S:= {$0..P[n]-1}:
  for k from 1 do
    S:= S minus {P[k+1] mod P[n]};
    if S = {} then return k fi;
  od
end proc;
map(f, [$2..100]); # Robert Israel, Nov 04 2025

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 *)

Crossrefs

Sequence in context: A018663 A110575 A325556 * A032664 A166733 A172987

Adjacent sequences: A174837 A174838 A174839 * A174841 A174842 A174843

Keyword

nonn

Author

Keith Backman, Mar 30 2010

Extensions

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

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

Offset corrected by Robert Israel, Nov 03 2025

Status

approved