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 A187188 Parse the infinite string 0123456789012345678901234567890... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 01, 23, 45, 67, 89, 012, 34, 56, 78, 90, 12, 345, ...; a(n) = length of n-th phrase. 12
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 12, 12, 12, 12, 12, 13, 12, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS See A187180-A187187 for further details. Answers a question raised by Sergio Verdu (personal communication, Mar 05 2011). LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1). FORMULA After the initial block of 10 1's, the sequence is quasi-periodic with period 100, increasing by 10 after each block. In more detail: a(n) = 1 for 1 <= n <= 10. For n >= 10, write n = 11 + 100i + j with i >= 0, 0 <= j <= 99. Then for 0 <= j <= 79, a(n) = 10i + f(j), where f(0) ... f(79) is the following 80-term sequence: [2   2   2   2   2   3   2   2   2   2   2   3 3   3   3   3   3   3   3   3 4   4   4   4   4   5   4   4   4   4   4   5 6   5   5   6   5   5   6   5   5   6   5   5 6   7 6   6   6   6   6 7   7   7   7   7   7   7   7   7 8   8   8   8   8   9   8   8   8   8   8   9 9   9   9   9   9   9   9   9] (this has been broken into blocks to make it easier to see), and for 80 <= j <= 99, a(n) = 10i+10 if j is even, a(n) = 10i+11 if j is odd. Examples: n=120 = 11 + 100*1 + 9, i=1, j=9, a(120)=10+f(9) = 10+2 = 12 n=292 = 11 + 100*2 + 81, i=2, j=81. a(292)=20+11=31 EXAMPLE The sequence begins 1   1   1   1   1   1   1   1   1   1 2   2   2   2   2   3   2   2   2   2   2   3 3   3   3   3   3   3   3   3 4   4   4   4   4   5   4   4   4   4   4   5 6   5   5   6   5   5   6   5   5   6   5   5 6   7 6   6   6   6   6 7   7   7   7   7   7   7   7   7 8   8   8   8   8   9   8   8   8   8   8   9 9   9   9   9   9   9   9   9 10  11  10  11  10  11  10  11  10  11 10  11  10  11  10  11  10  11  10  11 12  12  12  12  12  13  12  12  12  12  12  13 ... CROSSREFS See A187180-A187188 for alphabets of size 2 through 10. See also A109337, A187199, A187200. Sequence in context: A262813 A188794 A161966 * A183027 A078178 A306396 Adjacent sequences:  A187185 A187186 A187187 * A187189 A187190 A187191 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 06 2011 STATUS approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)