cp's OEIS Frontend

A204908 Least k such that n divides s(k)-s(j) for some j in [1,k], where s(k) is the k-th prime >=5.

%I A204908 #12 Apr 05 2023 13:50:57
%S A204908 2,2,3,3,5,3,6,4,7,5,8,5,9,6,10,7,11,7,12,9,13,8,14,8,16,9,15,11,18,
%T A204908 10,17,10,18,11,21,11,20,12,21,13,22,13,23,16,23,14,24,14,25,16
%N A204908 Least k such that n divides s(k)-s(j) for some j in [1,k], where s(k) is the k-th prime >=5.
%C A204908 See A204892 for a discussion and guide to related sequences.
%H A204908 Jinyuan Wang, <a href="/A204908/b204908.txt">Table of n, a(n) for n = 1..1000</a>
%t A204908 s[n_] := s[n] = Prime[n + 2]; z1 = 400; z2 = 50;
%t A204908 Table[s[n], {n, 1, 30}] (* primes >=5 *)
%t A204908 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A204908 Table[u[m], {m, 1, z1}]     (* A204906 *)
%t A204908 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A204908 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A204908 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A204908 Table[d[n], {n, 1, z2}]     (* A204907 *)
%t A204908 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A204908 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A204908 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A204908 Table[k[n], {n, 1, z2}]     (* A204908 *)
%t A204908 Table[j[n], {n, 1, z2}]     (* A204909 *)
%t A204908 Table[s[k[n]], {n, 1, z2}]  (* A204910 *)
%t A204908 Table[s[j[n]], {n, 1, z2}]  (* A204911 *)
%o A204908 (PARI) a(n) = {my(p=5, k=1); while(sum(i=5, p-1, isprime(i)&&(p-i)%n==0)==0, p=nextprime(p+1); k++); k; } \\ _Jinyuan Wang_, Jan 30 2020
%Y A204908 Cf. A000040, A204892, A204900.
%K A204908 nonn
%O A204908 1,1
%A A204908 _Clark Kimberling_, Jan 20 2012