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 A117127 Concatenate the first n positive integers written in binary (with each integer written so the most significant 1 is on the left and the concatenated string is from left to right). a(n) is the number of times n written in binary appears in the concatenated string. 3
 1, 1, 2, 1, 2, 3, 3, 1, 2, 1, 4, 3, 4, 5, 4, 1, 2, 2, 3, 2, 3, 2, 7, 3, 4, 4, 6, 6, 5, 7, 5, 1, 2, 2, 3, 1, 4, 3, 4, 2, 4, 2, 5, 2, 4, 4, 9, 3, 4, 5, 5, 4, 6, 4, 9, 6, 6, 6, 7, 9, 6, 9, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 5, 2, 6, 4, 5, 2, 4, 3, 6, 3, 5, 4, 7, 2, 5, 4, 7, 3, 7, 5, 11, 3, 4, 5, 5, 4, 7, 5, 7, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See also A047778, concatenation of first n numbers in binary. - Jonathan Vos Post, Apr 21 2006 Note that these counts reflect the pattern overlapping case. - Diana L. Mecum, Aug 06 2008 First occurrence of n: 1, 3, 6, 11, 14, 27, 23, 107, 47, 119, 95, 111, 191, 239, 223, 1007, 767, 447, 1535, 991, 895, 959, 3519, 1791, 1983, 1919, 3583, 7159, 7871, 3839, 14327, 16063, 8063, 7679, 7935, 15839, ??, 15359, 16127, 15871, ..., ; limit of search = 25000. - Robert G. Wilson v, Aug 30 2008 LINKS Diana Mecum and Robert G. Wilson v, Table of n, a(n) for n = 1..10000 EXAMPLE The first 13 positive integers written in binary and concatenated is 11011100101110111100010011010101111001101. 13 in binary, which is 1101, appears 4 times in the concatenated string, starting at positions (reading from left to right) 1, 12, 25 and 38. The last occurrence of 1101 is the integer 13 itself converted to binary and added to the end of the concatenated string, of course. So a(13) = 4. MAPLE A007088 := proc(n) convert(n, base, 2) ; ListTools[Reverse](%) ; end: A058935 := proc(n) local i, a ; if n = 0 then RETURN([0]) ; else a := [] ; for i from 1 to n do a := [op(a), op(A007088(i))] ; od: fi ; end: A117127 := proc(n) local a058935, strtL, endL, nL, a ; nL := A007088(n) ; a058935 := A058935(n) ; a := 0 ; for strtL from 1 to nops(a058935) do for endL from strtL to nops(a058935) do if verify[sublist]( nL, [op(strtL..endL, a058935)] ) then a := a+1 ; fi ; od: od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ", A117127(n)) ; od: # R. J. Mathar, Jan 23 2008 MATHEMATICA a[n_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> True]; Array[a, 105] (* Robert G. Wilson v, Aug 30 2008 *) fc[n_]:=Module[{idn2=IntegerDigits[n, 2], len}, len=Length[idn2]; Count[ Partition[ Flatten[Table[IntegerDigits[i, 2], {i, n}]], len, 1], idn2]]; Array[fc, 110] (* Harvey P. Dale, Dec 16 2011 *) CROSSREFS Cf. A007088, A030190, A058935, A047778, A141439. Sequence in context: A272917 A239627 A101933 * A278148 A136624 A033763 Adjacent sequences:  A117124 A117125 A117126 * A117128 A117129 A117130 KEYWORD easy,nonn,base AUTHOR Leroy Quet, Apr 20 2006 EXTENSIONS More terms from R. J. Mathar, Jan 23 2008 Terms 81 through 2000 from Diana L. Mecum, Aug 06 2008 STATUS approved

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)