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

%I A073325 #26 Mar 18 2023 18:35:41
%S A073325 1,2,3,4,75,9,79,18,17,10,19,20,91,22,23,41,83,24,16049,43,2711,94,25,
%T A073325 26,95,198,449,452,99,50,451,48,453,1072,447,54,16043,55,2719,56,459,
%U A073325 57,101,472,100371,62,105,102,103,104,467,110,107,65,109,63,115,118,117
%N A073325 a(n) = least k > 0 such that prime(k) == n (mod k).
%C A073325 First appearance of n-1 in A004648. Are all positive integers present in A004648 and hence in this sequence? - _Zak Seidov_, Sep 02 2012
%H A073325 Zak Seidov, <a href="/A073325/b073325.txt">Table of n, a(n) for n = 1..301</a>
%F A073325 a(n) = Min{x; Mod[A000040(x), x]=n} = Min{x; A004648[x]=n}.
%e A073325 a(4) = 75 as prime(75) = 379 == 4 (mod 75).
%e A073325 a(44) = 100371 since prime(100371) = 1304867 == 44 (mod 100371) and prime(k) <> 44 (mod k) for k < 100371.
%t A073325 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]
%t A073325 lk[n_]:=Module[{k=1},While[Mod[Prime[k],k]!=n,k++];k]; Array[lk,60,0] (* _Harvey P. Dale_, Nov 29 2013 *)
%o A073325 (PARI) stop=110000; for(n=0,59,k=1; while(k<stop&((prime(k)%k)!=n), k++); print1(if(k<stop,k,0),","))
%o A073325 (Python)
%o A073325 from sympy import prime, nextprime
%o A073325 def A073325(n):
%o A073325     p, m = prime(n), n
%o A073325     while p%m != n-1:
%o A073325         p = nextprime(p)
%o A073325         m += 1
%o A073325     return m # _Chai Wah Wu_, Mar 18 2023
%Y A073325 Cf. A000040, A002808, A004648, A073324, A073326.
%K A073325 nonn
%O A073325 1,2
%A A073325 _Labos Elemer_, Jul 30 2002
%E A073325 Definition revised by _N. J. A. Sloane_, Aug 12 2009
%E A073325 A216162 merged into this sequence by _T. D. Noe_, Sep 07 2012