A262986 Start of first run of length n in Golomb's sequence A001462.

1, 2, 6, 12, 24, 39, 63, 91, 123, 168, 218, 273, 345, 423, 507, 597, 709, 828, 954, 1087, 1247, 1415, 1591, 1775, 1991, 2216, 2450, 2693, 2945, 3235, 3535, 3845, 4165, 4495, 4869, 5254, 5650, 6057, 6475, 6943, 7423, 7915, 8419, 8935, 9463, 10048, 10646, 11257, 11881, 12518

Offset: 1

Author

Glen Whitney, Oct 06 2015

Keywords

• nonn

Comments

The first run of length n in A001462 begins with A095114(n), i.e., A001462(a(n)) = A095114(n).

a(n) = A095114(A095114(n)).

Examples

			Since Golomb's sequence starts 1,2,2,3,3,4,4,4,5,... the first run of length three starts at position 6, so a(3) = 6.
		

Crossrefs

Cf. A001462, A095114.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + a[n - a[a[n - 1]]]; s = Array[a, {13000}]; t = Most@ Map[Last, Tally@ s]; Table[Total@ Take[t, First@ Flatten@ Position[t, n]] - n + 1, {n, 50}] (* Michael De Vlieger, Oct 07 2015, after Robert G. Wilson v at A001462 *)

PARI

a(n) = if (n<2, 1, a(n-1)+ t(n-1)*(n-1));
t(n) = local(A, t, i); if(n<3, max(0, n), A=vector(n); t=A[i=2]=2; for(k=3, n, A[k]=A[k-1]+if(t--==0, t=A[i++ ]; 1)); A[n]);
vector(100, n, a(n))\\ Altug Alkan, Oct 06 2015

Formula

a(1) = 1; a(n+1) = a(n) + A001462(n)*n.

Extensions

More terms from Altug Alkan, Oct 06 2015