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

1,2

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(PARI) stop=110000; for(n=0, 59, k=1; while(k<stop&((prime(k)%k)!=n), k++); print1(if(k<stop, k, 0), ", "))
(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

Crossrefs

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

Sequence in context: A076519 A066776 A115901 * A142959 A173573 A037395

Adjacent sequences: A073322 A073323 A073324 * A073326 A073327 A073328

Keyword

nonn

Author

Labos Elemer, Jul 30 2002

Extensions

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

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

Status

approved