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%I #20 Feb 17 2017 04:20:44
%S 3,5,7,15,22,17,19,48,23,41,82,39,29,47,77,94,53,91,112,69,81,61,59,
%T 101,189,142,103,85,107,109,203,354,148,95,1122,158,169,141,119,127,
%U 166,241,226,491,131,125,137,185,251,393,242,133,332,139,244,340,402
%N a(n) is the smallest number k such that prime(k) == 2*n-1 (mod phi(k)).
%C From _Michael De Vlieger_, Feb 16 2017: (Start)
%C Records and position of records:
%C 3 1
%C 5 2
%C 7 3
%C 15 4
%C 22 5
%C 48 8
%C 82 11
%C 94 16
%C 112 19
%C 189 25
%C 203 31
%C 354 32
%C 1122 35
%C 1223 74
%C 1234 103
%C 4244 104
%C 6718 137
%C 12218 200
%C 16304 218
%C 19540 248
%C 74478 263
%C 1014994 323
%C 2801012 1268
%C 16829184 1913
%C 16903906 2213
%C a(2468) is larger than 10^8. (End)
%H Michael De Vlieger and Michel Marcus, <a href="/A071169/b071169.txt">Table of n, a(n) for n = 1..2467</a> (First 262 terms from Michel Marcus), Feb 16 2017
%F a(n) = Min_{k} A071168(k) = 2*n-1.
%e n=5, a(5)=22, prime(22)=79, Phi[22]=10, Mod[79,10]=9=2n-1=5.
%t f[x_] := Mod[Prime[x], EulerPhi[x]] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t
%t (* Second program: *)
%t Table[x = 1; While[Mod[Prime@ x, EulerPhi@ x] != 2 n - 1, x++]; x, {n, 57}] (* _Michael De Vlieger_, Feb 13 2017 *)
%o (PARI) a(n) = {my(x = 1); while (prime(x) % eulerphi(x) != 2*n-1, x++); x;} \\ _Michel Marcus_, Feb 13 2017
%Y Cf. A000040, A000010, A066936, A071168.
%K nonn
%O 1,1
%A _Labos Elemer_, May 15 2002
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