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A071169 a(n) is the smallest number k such that prime(k) == 2*n-1 (mod phi(k)). 2
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 (list; graph; refs; listen; history; text; internal format)
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=5.

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

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)