The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309523 Start with a(1) = 1 and apply certain patterns of operations on a(n-1) to obtain a(n) as described in comments. 1
 1, 7, 8, 2, 16, 4, 5, 17, 10, 34, 35, 11, 70, 22, 23, 71, 46, 142, 143, 47, 286, 94, 95, 287, 190, 574, 575, 191, 1150, 382, 383, 1151, 766, 2302, 2303, 767, 4606, 1534, 1535, 4607, 3070, 9214, 9215, 3071, 18430, 6142, 6143, 18431, 12286, 36862 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(2) = 7 is obtained from a(1) = 1 by (((1) +1) *3) +1. We abbreviate this to the operation pattern "+1 *3 +1". The 8 patterns for a(3..10), a(11..18) etc. are:   +1   +1 /3 -1   +1 *3 *2 -2   -1 /3 -1   +1   +1 *3 -1   +1 /3 *2 -2   +1 *3 +1 A308709 uses similar, but simpler patterns in blocks of 4 (cf. the example, below). A308709 contains the set {2^k | k>=0} union {3*2^k | k>=0}, so all terms are different. This sequence contains the terms {6*A308709 - 2} union {6*A308709 - 1}, therefore all terms are also different. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,-1,1,0,0,0,0,4,-4,4,-4). FORMULA From Colin Barker, Aug 06 2019: (Start) G.f.: x*(1 + 6*x + 2*x^2 + 15*x^4 - 18*x^5 + 15*x^6 - 10*x^8 + 12*x^9 - 14*x^10) / ((1 - x)*(1 + x^2)*(1 - 2*x^4)*(1 + 2*x^4)). a(n) = a(n-1) - a(n-2) + a(n-3) + 4*a(n-8) - 4*a(n-9) + 4*a(n-10) - 4*a(n-11) for n>11. (End) EXAMPLE A308709 | this sequence           |   1           |   7    +1 *3 +1           |   8    +1           |   2    +1 /3 -1    3      |  16    +1 *3 *2 -2    1   /3 |   4    -1 /3 -1           |   5    +1           |  17    +1 *3 -1    2   *2 |  10    +1 /3 *2 -2    6   *3 |  34    +1 *3 +1           |  35    +1           |  11    +1 /3 -1   12   *2 |  70    +1 *3 *2 -2    4   /3 |  22    -1 /3 -1           |  23    +1           |  71    +1 *3 -1    8   *2 |  46    +1 /3 *2 -2   24   *3 | 142    +1 *3 +1           | 143    +1 MATHEMATICA LinearRecurrence[{1, -1, 1, 0, 0, 0, 0, 4, -4, 4, -4}, {1, 7, 8, 2, 16, 4, 5, 17, 10, 34, 35}, 50] PROG (PARI) Vec(x*(1 + 6*x + 2*x^2 + 15*x^4 - 18*x^5 + 15*x^6 - 10*x^8 + 12*x^9 - 14*x^10) / ((1 - x)*(1 + x^2)*(1 - 2*x^4)*(1 + 2*x^4)) + O(x^40)) \\ Colin Barker, Aug 06 2019 (Perl) use integer;   my @a; my \$n = 1; \$a[\$n ++] = 1;   \$a[\$n ++] =   ((\$a[\$n-1] +1) *3) +1;    #  7   while (\$n < 50) {     \$a[\$n ++] = ((\$a[\$n-1] +1)   );       #  8     \$a[\$n ++] = ((\$a[\$n-1] +1) /3) -1;    #  2     \$a[\$n ++] = ((\$a[\$n-1] +1) *3) *2 -2; # 16     \$a[\$n ++] = ((\$a[\$n-1] -1) /3) -1;    #  4     \$a[\$n ++] = ((\$a[\$n-1] +1)   );       #  5     \$a[\$n ++] = ((\$a[\$n-1] +1) *3) -1;    # 17     \$a[\$n ++] = ((\$a[\$n-1] +1) /3) *2 -2; # 10     \$a[\$n ++] = ((\$a[\$n-1] +1) *3) +1;    # 34   } # while   shift(@a); # remove \$a[0]   print join(", ", @a) . "\n"; # Georg Fischer, Aug 07 2019 (Python 3) def A309523():     k, j, a = 0, 0, 1     def b(a): return a + 1     def c(a): return a + 2     def d(a): return a - 1     def e(a): return a - 2     def f(a): return a << 1     def g(a): return a * 3     def h(a): return a // 3     O = [c, g, e, b, b, h, d, b, g, f, e, c, h, e, b, b, g, d, b, h, f, e]     L = [3, 1, 3, 4]     while True:         yield(a)         for _ in range(L[j]):             a = O[k](a)             k += 1; k %= 22         j += 1; j %= 4 a = A309523() print([next(a) for _ in range(50)]) # Peter Luschny, Aug 06 2019 CROSSREFS Cf. A308709. Sequence in context: A342486 A245758 A266566 * A153622 A257576 A064207 Adjacent sequences:  A309520 A309521 A309522 * A309524 A309525 A309526 KEYWORD nonn,easy AUTHOR Georg Fischer, Aug 06 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)