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A178215
a(n) is the least number such that the set {p_1,p_2,...,p_a(n)} contains all residues modulo p_n (where p_m is m-th prime).
2
2, 4, 8, 10, 14, 27, 27, 43, 33, 66, 64, 85, 75, 90, 163, 111, 127, 178, 170, 145, 172, 215, 197, 238, 239, 324, 298, 364, 345, 328, 516, 442, 544, 421, 482, 613, 495, 605, 544, 647, 553, 646, 645, 520, 743, 594, 738, 645, 852, 1013, 788, 1205, 728, 900, 801, 1047
OFFSET
1,1
EXAMPLE
If n=3, then p_n=5 and we see that {2,3,5,7,11,13,17,19} is the minimal set of the first primes, which contains all residues modulo 5 (we have consecutive residues {2,3,0,2,1,3,2,4}. Therefore a(3)=8.
MATHEMATICA
Table[k = 1; While[Union@ Mod[Prime@ Range@ k, #] != Range[0, # - 1], k++] &@ Prime@ n; k, {n, 56}] (* Michael De Vlieger, May 16 2017 *)
CROSSREFS
Cf. A000040.
Sequence in context: A242247 A089033 A049422 * A067925 A323102 A331627
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 22 2010
EXTENSIONS
a(10) corrected and a(11)-a(56) from Donovan Johnson, Jun 23 2010
STATUS
approved