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 A336683 Sum of 2^k for all residues k found in the Fibonacci sequence mod n. 2
 1, 3, 7, 15, 31, 63, 127, 175, 511, 1023, 1327, 4031, 7471, 16383, 32767, 43951, 127807, 238895, 502063, 1048575, 1319215, 2719023, 7798639, 10692015, 33554431, 61209903, 134217727, 259173375, 337649967, 1073741823, 1571892655, 2880154543, 5417565487, 15638470959 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n of A079002 compactified as a binary number. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..3322 Michael De Vlieger, Plot of bits of a(n) beginning with 2^0 at left for 1 <= n <= 5000. FORMULA a(n) = Sum(2^k) for all k in row n of A189768. a(n) = 2^(n+1) - 1 for n in A079002. EXAMPLE a(1) = 1 by convention. a(2) = 3 = 2^0 + 2^1, since the Fibonacci sequence mod 2 is {0,1,1} repeated, and 0 and 1 appear in the sequence. a(8) = 175 = 2^0 + 2^1 + 2^2 + 2^3 + 2^5 + 2^7, since the Fibonacci sequence mod 8 is {0,1,1,2,3,5,0,5,5,2,7,1} repeated, and we are missing 4 and 6, leaving the exponents of 2 as shown. Binary equivalents of first terms: n a(n) a(n) in binary -------------------------- 1 1 1 2 3 11 3 7 111 4 15 1111 5 31 11111 6 63 111111 7 127 1111111 8 175 10101111 9 511 111111111 10 1023 1111111111 11 1327 10100101111 12 4031 111110111111 13 7471 1110100101111 14 16383 11111111111111 15 32767 111111111111111 16 43951 1010101110101111 ... MATHEMATICA {1}~Join~Array[Block[{w = {0, 1}}, Do[If[SequenceCount[w, {0, 1}] == 1, AppendTo[w, Mod[Total@ w[[-2 ;; -1]], #]], Break[]], {i, 2, Infinity}]; Total[2^Union@ w]] &, 33, 2] (* Second program: generate the first n terms using the plot in Links *) With[{n = 34, img = ImageData@ ColorNegate@ Import["https://oeis.org/A336683/a336683.png"]}, Map[FromDigits[#, 2] &@ Drop[#, LengthWhile[#, # == 0 &]] &@ Reverse[IntegerPart[#]] &, img[[1 ;; n]]]] (* Michael De Vlieger, Oct 05 2020 *) CROSSREFS Cf. A000045, A001175, A066853, A079002, A128924, A189768. Sequence in context: A275715 A273672 A043740 * A283091 A277716 A116082 Adjacent sequences: A336680 A336681 A336682 * A336684 A336685 A336686 KEYWORD nonn,easy AUTHOR Michael De Vlieger, Oct 04 2020 STATUS approved

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Last modified November 28 17:03 EST 2023. Contains 367419 sequences. (Running on oeis4.)