A071169 a(n) is the smallest number k such that prime(k) == 2*n-1 (mod phi(k)).

3, 5, 7, 15, 22, 17, 19, 48, 23, 41, 82, 39, 29, 47, 77, 94, 53, 91, 112, 69, 81, 61, 59, 101, 189, 142, 103, 85, 107, 109, 203, 354, 148, 95, 1122, 158, 169, 141, 119, 127, 166, 241, 226, 491, 131, 125, 137, 185, 251, 393, 242, 133, 332, 139, 244, 340, 402

Offset

1,1

Comments

From Michael De Vlieger, Feb 16 2017: (Start)

Records and position of records:

3 1

5 2

7 3

15 4

22 5

48 8

82 11

94 16

112 19

189 25

203 31

354 32

1122 35

1223 74

1234 103

4244 104

6718 137

12218 200

16304 218

19540 248

74478 263

1014994 323

2801012 1268

16829184 1913

16903906 2213

a(2468) is larger than 10^8. (End)

Links

Michael De Vlieger and Michel Marcus, Table of n, a(n) for n = 1..2467 (First 262 terms from Michel Marcus), Feb 16 2017

Formula

a(n) = Min_{k} A071168(k) = 2*n-1.

Example

n=5, a(5)=22, prime(22)=79, phi(22)=10, mod(79,10)=9=2n-1=9.

Mathematica

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
(* Second program: *)
Table[x = 1; While[Mod[Prime@ x, EulerPhi@ x] != 2 n - 1, x++]; x, {n, 57}] (* Michael De Vlieger, Feb 13 2017 *)

Prog

(PARI) a(n) = {my(x = 1); while (prime(x) % eulerphi(x) != 2*n-1, x++); x; } \\ Michel Marcus, Feb 13 2017

Crossrefs

Cf. A000040, A000010, A066936, A071168.

Sequence in context: A018286 A194360 A057743 * A172235 A163979 A124248

Adjacent sequences: A071166 A071167 A071168 * A071170 A071171 A071172

Keyword

nonn

Author

Labos Elemer, May 15 2002

Status

approved