A073325 a(n) = least k > 0 such that prime(k) == n (mod k).

1, 2, 3, 4, 75, 9, 79, 18, 17, 10, 19, 20, 91, 22, 23, 41, 83, 24, 16049, 43, 2711, 94, 25, 26, 95, 198, 449, 452, 99, 50, 451, 48, 453, 1072, 447, 54, 16043, 55, 2719, 56, 459, 57, 101, 472, 100371, 62, 105, 102, 103, 104, 467, 110, 107, 65, 109, 63, 115, 118, 117

Offset: 1

Author

Labos Elemer, Jul 30 2002

Keywords

• nonn

Comments

First appearance of n-1 in A004648. Are all positive integers present in A004648 and hence in this sequence? - Zak Seidov, Sep 02 2012

Examples

			a(4) = 75 as prime(75) = 379 == 4 (mod 75).
a(44) = 100371 since prime(100371) = 1304867 == 44 (mod 100371) and prime(k) <> 44 (mod k) for k < 100371.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..301

Crossrefs

Cf. A000040, A002808, A004648, A073324, A073326.

Programs

Mathematica

nn = 60; f[x_] := Mod[Prime[x], x]; t = Table[0, {nn}]; k = 0; While[Times @@ t == 0, k++; n = f[k]; If[n <= nn && t[[n]] == 0, t[[n]] = k]]; Join[{1}, t]
lk[n_]:=Module[{k=1},While[Mod[Prime[k],k]!=n,k++];k]; Array[lk,60,0] (* Harvey P. Dale, Nov 29 2013 *)

PARI

stop=110000; for(n=0,59,k=1; while(k
				

Python

from sympy import prime, nextprime
def A073325(n):
    p, m = prime(n), n
    while p%m != n-1:
        p = nextprime(p)
        m += 1
    return m # Chai Wah Wu, Mar 18 2023

Formula

a(n) = Min{x; Mod[A000040(x), x]=n} = Min{x; A004648[x]=n}.

Extensions

Definition revised by N. J. A. Sloane, Aug 12 2009

A216162 merged into this sequence by T. D. Noe, Sep 07 2012