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A237643 Least positive integer m such that {A000720(k*n): k = 1, ..., m} contains a complete system of residues modulo n, or 0 if such a number m does not exist. 4
1, 2, 3, 8, 8, 12, 13, 14, 27, 25, 32, 25, 16, 23, 94, 41, 46, 67, 38, 60, 77, 55, 84, 46, 88, 79, 85, 113, 82, 155, 114, 141, 178, 132, 124, 176, 155, 96, 135, 176, 146, 148, 126, 125, 183, 191, 185, 194, 166, 261, 378, 230, 278, 203, 199, 161, 293, 286, 175, 274 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: a(n) is always positive. Moreover, a(n) <= 2*prime(n) for all n > 0.

Note that a(15) = 94 = 2*prime(15).

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Zhi-Wei Sun, On a^n+bn modulo m, preprint, arXiv:1312.1166 [math.NT], 2013-2014.

EXAMPLE

a(4) = 8 since {A000720(4*k): k = 1, ..., 8} = {2, 4, 5, 6, 8, 9, 9, 11} contains a complete system of residues modulo 4, but {pi(4*k}: k = 1, ..., 7} contains no integer congruent to 3 modulo 4.

MATHEMATICA

q[m_, n_]:=Length[Union[Table[Mod[PrimePi[k*n], n], {k, 1, m}]]]

Do[Do[If[q[m, n]==n, Print[n, " ", m]; Goto[aa]], {m, n, 2*Prime[n]}];

Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 60}]

CROSSREFS

Cf. A000720, A237578, A237597, A237598, A237612, A237614, A237656.

Sequence in context: A100836 A173162 A198104 * A225474 A329432 A100805

Adjacent sequences:  A237640 A237641 A237642 * A237644 A237645 A237646

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 10 2014

STATUS

approved

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Last modified May 16 07:30 EDT 2022. Contains 353693 sequences. (Running on oeis4.)