I submitted the following trivalued sequence, based on the Dragon Curve. I don't see a connection with any of its suggestions. ? —rwg ---------- Forwarded message --------- From: <superseeker-reply@oeis.org> Date: Wed, Sep 11, 2019 at 7:14 PM Subject: Re: To: <billgosper@gmail.com> Greetings from The On-Line Encyclopedia of Integer Sequences! https://oeis.org/
lookup 2 1 3 2 1 2 3 2 2 1 2 3 1 2 3 2 2 1 3 2 1 2 2 3 2 1 2 3 1
a(n) = 2, 1, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 2, 3, 2, 1, 2, 3, 1 Note: Your sequence does not directly appear in the OEIS. If it is of general interest, please submit it at https://oeis.org/Submit.html. # Transformations These sequences match transformations of the original query. T099 abs(a(n)), sorted with duplicates removed = 1, 2, 3 oeis.org/A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. 0, 1, <1, 2, 3>, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155 oeis.org/A000041 a(n) is the number of partitions of n (the partition numbers). 1, <1, 2, 3>, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525 oeis.org/A000027 The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous. <1, 2, 3>, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77 oeis.org/A001222 Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)). 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, <1, 2, 3>, 6, 2, 3, 1, 3, 2, 3, 1, 5, <1, 2, 3>, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 3, 1, 4, 3, 2, 1, 5, 1, 3, 2 oeis.org/A001221 Number of distinct primes dividing n (also called omega(n)). 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, <1, 2, 3>, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, <1, 2, 3>, 2, 1, 2, 1, 3, 2 ... 25666 total # Transformations as Deltas The deltas of these sequences match transformations of the original query. T030 a(n+2) - a(n) = 1, 1, 2, 0, 2, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 0, 2, 1 (as deltas) oeis.org/A301849 The Pagoda sequence: a sequence with isolated zeros in number-wall over finite fields. -1, 0, <1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0>, 1, -1, -1, 0, 1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, 0, -1, -1, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0, 1, -1, -1, 0, <1, 0, -1, 1, 1, -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 0, -1, 1, 1, 0, -1, -1, 1, 1, -1, 0>, 1, 0, -1, -1, 1, 0 oeis.org/A253414 G.f. satisfies (1+x^2)*g(x) = 1 + x*g(x^2). 1, 1, <-1, 0, 1, -1, -1, 1, 1, 0, -1, -1, 1, 0, -1, 1, 1, 0, -1, 0, 1, -1, -1, 0, 1, 1, -1, -1, 1, 0>, -1, 1, 1, 0, -1, 0, 1, -1, -1, 1, 1, 0, -1, -1, 1, 0, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, 1, 1, -1, -1, 1, 0, -1, 1, 1, 0, <-1, 0, 1, -1, -1, 1, 1, 0, -1, -1, 1, 0, -1, 1, 1, 0, -1, 0, 1, -1, -1, 0, 1, 1, -1, -1, 1, 0>, -1, 0, 1, 1, -1, 0, 1 T035 a(n) + 2 = 4, 3, 5, 4, 3, 4, 5, 4, 4, 3, 4, 5, 3, 4, 5, 4, 4, 3, 5, 4, 3, 4, 4, 5, 4, 3, 4, 5, 3 (as deltas) oeis.org/A317331 Indices m for which A058304(m) = 1. <4, 8, 11, 16, 20, 23, 27, 32, 36, 40, 43, 47, 52, 55, 59, 64, 68, 72, 75, 80, 84, 87, 91, 95, 100, 104, 107, 111, 116, 119>, 123, 128, 132, 136, 139, 144, 148, 151, 155, 160, 164, 168, 171, 175, 180, 183, 187, 191, 196, 200, 203, 208, 212, 215, 219, 223, 228, 232, 235, 239, 244, 247, 251 T038 a(n) - 2 = 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1 (as deltas) oeis.org/A014577 The regular paper-folding sequence (or dragon curve sequence). <1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0>, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, <1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0>, 0, 0, 1, 1, 0 oeis.org/A038189 Bit to left of least significant 1-bit in binary expansion of n. 0, <0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1>, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, <0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1>, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1 oeis.org/A014707 a(4n)=0, a(4n+2)=1, a(2n+1)=a(n). <0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1>, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0 oeis.org/A082410 a(1)=0. Thereafter, the sequence is constructed using the rule: for any k >= 0, if a(1), a(2), ..., a(2^k+1) are known, the next 2^k terms are given as follows: a(2^k+1+i) = 1 - a(2^k+1-i) for 1 <= i <= 2^k. 0, <1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0>, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, <1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0>, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1 oeis.org/A014710 The regular paper-folding (or dragon curve) sequence. <2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1>, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2 ... 9 total T099 abs(a(n)), sorted with duplicates removed = 1, 2, 3 (as deltas) oeis.org/A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. 0, 1, 1, <2, 3, 5, 8>, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155 oeis.org/A000217 Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n. <0, 1, 3, 6>, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431 oeis.org/A001222 Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)). 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, <2, 3, 1, 4>, 2, 4, 2, 2, 1, 4, 1, 2, 3, 6, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 3, 1, 4, 3, 2, 1, 5, 1, 3, 2 oeis.org/A000700 Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes. 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 11, 12, 12, 14, 16, <17, 18, 20, 23>, 25, 26, 29, 33, 35, 37, 41, 46, 49, 52, 57, 63, 68, 72, 78, 87, 93, 98, 107, 117, 125, 133, 144, 157, 168, 178, 192, 209, 223, 236, 255, 276, 294, 312, 335, 361, 385 oeis.org/A112798 Table where n-th row is factorization of n, with each prime p_i replaced by i. 1, 2, 1, 1, 3, <1, 2, 4, 1>, 1, 1, 2, 2, 1, 3, 5, 1, 1, 2, 6, 1, 4, 2, 3, 1, 1, 1, 1, 7, 1, 2, 2, 8, 1, 1, <3, 2, 4, 1>, 5, 9, 1, 1, 1, 2, 3, 3, 1, 6, 2, 2, 2, 1, 1, 4, 10, 1, 2, 3, 11, 1, 1, 1, 1, 1, 2, 5, 1, 7, 3, 4, 1, 1, 2, 2, 12, 1, 8, 2, 6, 1, 1, 1, 3, 13, 1, 2, 4, 14, 1, 1, 5, 2, 2, 3, 1, 9, 15, 1, 1, 1, 1 ... 17444 total In transformation descriptions, Sn(z) denotes the ordinary generating function with coefficients a(n), and En(z) denotes the exponential generating function with coefficients a(n). ___________________________________________________________________________ o You can look up sequences online at the OEIS web site https://oeis.org/ o For an explanation of the format used in the OEIS, see https://oeis.org/wiki/Style_Sheet o If your sequence was not in the OEIS and is of general interest, please submit it using the submission form https://oeis.org/Submit.html o The email address <sequences@oeis.org> does a simple lookup in the On-Line Encyclopedia of Integer Sequences, a limited form of the search available on the web site. o If you send an empty message, you will be sent the help file. 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