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A262986 Start of first run of length n in Golomb's sequence A001462. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 22 22:22 EDT 2019. Contains 322378 sequences. (Running on oeis4.)