A273943 Put and say how often: a(n) = n/2 if n is even, else a(n) = number of matches of "a(n-1)" in the concatenation of all "a(i)" with i < n, where "x" denotes the decimal string of x.

0, 1, 1, 2, 2, 2, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 4, 12, 2, 13, 1, 14, 3, 15, 2, 16, 2, 17, 2, 18, 2, 19, 2, 20, 1, 21, 6, 22, 5, 23, 2, 24, 1, 25, 2, 26, 1, 27, 1, 28, 1, 29, 1, 30, 1, 31, 4, 32, 2, 33, 1, 34, 1, 35, 1, 36, 1, 37, 1, 38, 1, 39, 1, 40, 1, 41, 5, 42, 1, 43, 3, 44, 1, 45, 1, 46, 1, 47, 1, 48, 1, 49, 1, 50, 1, 51, 4, 52, 4, 53, 1, 54, 2

Offset

0,4

Comments

Inspired by Look-and-Say sequences.

Links

Rainer Rosenthal, Table of n, a(n) for n = 0..106473

Example

a(4) = 2 by definition and a(5) = 2 because "2" appears twice in the string built from the first 5 entries, i.e. "01122".
Nice question: how to continue 0112223141516171819110111? Answer: 4, since 11 was put last and there are 4 occurrences of 11 so far.

Maple

rev:=proc(f)local i, fr; fr:=[]; for i to nops(f) do fr:=[op(fr), f[-i]]od; return fr; end:mc := z->`if`(z=0, [0], rev(convert(z, base, 10))):
matches := proc(f, z)local i, t, cnt; t:=mc(z); cnt:=0; for i to nops(f)+1-nops(t)do if f[i..i+nops(t)-1]=t then cnt := cnt+1; fi; od; return cnt; end:
addZ := proc(f, z)local t; t:=mc(z); return[op(f), op(t)]; end:
s:=[]:a:=[]:for i from 0 to 54 do s:=addZ(s, i); m:=matches(s, i); s:=addZ(s, m); a:=[op(a), i, m]; od:seq(a[i+1], i=0..109);

Crossrefs

Cf. A005150, A225212.

See A274013 for bisection a(2k+1).

Sequence in context: A141059 A135151 A256855 * A256071 A248808 A233206

Adjacent sequences: A273940 A273941 A273942 * A273944 A273945 A273946

Keyword

nonn,base,easy

Author

Rainer Rosenthal, Jun 05 2016

Status

approved