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A178215
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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).
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2
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Table[k = 1; While[Union@ Mod[Prime@ Range@ k, #] != Range[0, # - 1], k++] &@ Prime@ n; k, {n, 56}] (* Michael De Vlieger, May 16 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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