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

1,2

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)).

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A001462, A095114.

Sequence in context: A210594 A307252 A306625 * A307559 A211978 A028923

Adjacent sequences: A262983 A262984 A262985 * A262987 A262988 A262989

Keyword

nonn

Author

Glen Whitney, Oct 06 2015

Extensions

More terms from Altug Alkan, Oct 06 2015

Status

approved