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%I #13 Mar 05 2024 07:10:58
%S 21,22,23,45,47,55,73,85,86,90,91,95,109,110,111,119,146,170,173,181,
%T 182,187,191,219,221,223,239,247,273,307,341,342,346,362,365,375,383,
%U 409,438,443,447,477,478,479,495,503,546,585,614,660,682,685,693,725
%N Positions at which disjoint pattern counts differ from overlapping pattern counts related to sequence A117127.
%H Diana Mecum, <a href="/A141439/b141439.txt">Table of n, a(n) for n = 1..131</a>
%e When "n" = 21, the base two concatenated range of integers from 1 to 21 is "1101110010111011110001001101010111100110111101111100001000110010100111010010101". 21 in base two is "10101".
%e Note that there are two instances of "10101" in the concatenated number when disjoint patterns are considered. There are three pattern matches when overlapping patterns are considered.
%t f[n_, k_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> {True, False}[[k]]]; Select[ Range@ 725, f[ #, 1] != f[ #, 2] &] (* _Robert G. Wilson v_, Aug 30 2008 *)
%Y Cf. A117127.
%K nonn,base
%O 1,1
%A _Diana L. Mecum_, Aug 06 2008