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a(n) = smallest k such that A366475(k) >= n, or -1 if no such k exists.
3

%I #17 Oct 28 2023 14:40:57

%S 2,3,29,28025,2467754261

%N a(n) = smallest k such that A366475(k) >= n, or -1 if no such k exists.

%t nn = 2^16; c[_] := False; m[_] := 0; j = 1; c[0] = c[1] = True; q[_] := 0; s = -1;

%t Monitor[Do[p = Prime[n - 1]; r = Mod[j, p];

%t While[Set[k, p m[p] + r ]; c[k], m[p]++];

%t (If[q[#] == 0, Set[q[#], n]]; If[# > s, s = #]) &[ m[p] ];

%t Set[{c[k], j}, {True, k}], {n, 2, nn}], n];

%t Array[q, s] (* _Michael De Vlieger_, Oct 27 2023 *)

%o (Python)

%o from itertools import count

%o from sympy import nextprime

%o def A366477(n):

%o a, aset, p = 1, {0,1}, 1

%o for i in count(2):

%o p = nextprime(p)

%o b = a%p

%o for j in count(0):

%o if b not in aset:

%o aset.add(b)

%o a = b

%o break

%o b += p

%o if j>=n:

%o return i # _Chai Wah Wu_, Oct 27 2023

%Y Cf. A364054, A366475.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Oct 26 2023

%E a(4) = 28025 from _Michael De Vlieger_, Oct 26 2023, who also reports that 5 does not appear in the first 2^24 terms of A366475.

%E a(5) from _Chai Wah Wu_, Oct 28 2023