Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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