A205002
Least k such that n divides s(k)-s(j) for some j satisfying 1<=j
2, 2, 3, 4, 3, 5, 4, 8, 4, 6, 6, 5, 7, 5, 6, 16, 9, 6, 10, 6, 8, 7, 12, 9, 7, 8, 7, 11, 15, 8, 16, 32, 8, 10, 8, 12, 19, 11, 9, 10, 21, 9, 22, 9, 10, 13, 24, 17, 10, 12, 11, 10, 27, 10, 13, 11, 12, 16, 30, 11, 31, 17, 11, 64, 11, 17, 34, 12, 14, 13, 36, 12, 37, 20, 12, 13, 12, 18, 40, 18, 13, 22, 42, 14, 13, 23, 17, 13, 45, 13, 16, 15
Offset: 1
Keywords
Examples
(See example at A205001.)
Links
- Antti Karttunen, Table of n, a(n) for n = 1..11001
Programs
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Mathematica
s[n_] := s[n] = Binomial[n + 1, 2]; z1 = 500; z2 = 60; Table[s[n], {n, 1, 30}] (* A000217 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}] (* A193974 ? *) v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0] w[n_] := w[n] = Table[v[n, h], {h, 1, z1}] d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]] Table[d[n], {n, 1, z2}] (* A205001 *) k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2] m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2] j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2 Table[k[n], {n, 1, z2}] (* A205002 *) Table[j[n], {n, 1, z2}] (* A205003 *) Table[s[k[n]], {n, 1, z2}] (* A205004 *) Table[s[j[n]], {n, 1, z2}] (* A205005 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205006 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205007 *) -
PARI
A205002(n) = for(k=2,oo,my(sk=binomial(k+1,2)); for(j=1,k-1,if(!((sk-binomial(j+1,2))%n),return(k)))); \\ Antti Karttunen, Sep 27 2018
Extensions
More terms from Antti Karttunen, Sep 27 2018
Comments