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 A100002 Start with a sequence of 1's, then replace every other 1 with a 2; then replace every third of the remaining 1's with a 3 and every third of the remaining 2's with a 3; then replace every fourth remaining 1, 2 or 3 with a 4; and so on. The limiting sequence is shown here. 6
 1, 2, 1, 2, 3, 3, 1, 2, 4, 4, 3, 4, 1, 2, 5, 5, 3, 5, 1, 2, 4, 5, 3, 4, 6, 6, 1, 2, 6, 3, 7, 7, 6, 4, 7, 7, 5, 6, 1, 2, 5, 3, 8, 8, 7, 4, 8, 8, 1, 2, 6, 7, 3, 6, 5, 8, 4, 8, 5, 6, 9, 9, 1, 2, 9, 3, 10, 10, 9, 4, 10, 10, 7, 8, 9, 5, 7, 10, 1, 2, 9, 7, 3, 4, 9, 6, 11, 11, 10, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The position of the 1's is given by A000960. - T. D. Noe, Oct 26 2004 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 T. D. Noe, Plot of first 5000 terms A post on sci.math.research newsgroup. FORMULA a(1, j)=1 for all j>=1; a(n, j)=a(n-1, j) except when #{i<=j s.t. a(n-1, i)=a(n-1, j)} is multiple of n, in which case a(n, j)=n; a(j) is the limit of the (stationary) a(n, j) when n tends to infinity. It appears that the maximal value among the first n terms grows like sqrt(4n/3). Note that the first occurrence of n is bounded by A000960; that is, A100287(n) <= A000960(n), with equality only for n=1. - T. D. Noe, Nov 12 2004 EXAMPLE Here are the first 6 stages in the construction:   1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...   1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2...   1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3...   1 2 1 2 3 3 1 2 4 4 3 4 1 2 1 2 3 3 1 2 4 4 3 4 1 2 1 2 3 3...   1 2 1 2 3 3 1 2 4 4 3 4 1 2 5 5 3 5 1 2 4 5 3 4 1 2 1 2 3 3...   1 2 1 2 3 3 1 2 4 4 3 4 1 2 5 5 3 5 1 2 4 5 3 4 6 6 1 2 6 3...   ... MATHEMATICA nn=100; t=Table[1, {nn}]; done=False; k=1; While[ !done, k++; cnt=Table[0, {k-1}]; Do[If[t[[i]] b2]], b1, Range[b2 - 1]]], Array[1 &, n], Range[2, 2 Sqrt[n/Pi] + 1]]; a[100] (* Birkas Gyorgy, Feb 06 2011 *) PROG /* C */ #define MAXVAL 2048 /* Large enough... */ unsigned int counts[MAXVAL][MAXVAL]; /* Initialized at all 0 */ unsigned int seq_value (void) /* Successive calls return values in the sequence, in order. */ { unsigned int value; unsigned int i; value = 1; for ( i=2; i= i ) { counts[i][value] = 0; value = i; } return value; } CROSSREFS Cf. A100287 (first occurrence of n). Sequence in context: A071766 A007305 A112531 * A348330 A328471 A227909 Adjacent sequences:  A099999 A100000 A100001 * A100003 A100004 A100005 KEYWORD easy,nice,nonn AUTHOR David A. Madore, Oct 25 2004 STATUS approved

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Last modified January 21 00:11 EST 2022. Contains 350473 sequences. (Running on oeis4.)