

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 mth 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
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OFFSET

1,1


LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000
Zak Seidov, Graph of 1000 terms


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
Adjacent sequences: A178212 A178213 A178214 * A178216 A178217 A178218


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



