A000202 a(8i+j) = 13i + a(j), where 1<=j<=8.
1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 64, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 103, 105, 107, 108, 110
Offset: 1
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- James F. Peters, Problem H-327, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 19, No. 2 (1981), p. 189; Are You Curious?, Solution to Problem H-327 by Paul S. Bruckman, ibid., Vol. 20, No. 4 (1982), pp. 373-375.
- D. E. Thoro, Problem H-12, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 1, No. 2 (1963), p. 54; A Curious Sequence, Solution to Problem H-12 by Malcolm Tallman, ibid., Vol. 1, No. 4 (1963), p. 50.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).
Programs
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Maple
a[0] := 0:a[1] := 1:a[2] := 3:a[3] := 4:a[4] := 6:a[5] := 8:a[6] := 9:a[7] := 11:a[8] := 12: for m from 9 to 200 do if irem(m,8)=0 then myrem := 8; myquo := iquo(m,8)-1; else myrem := irem(m,8); myquo := iquo(m,8) fi; a[m] := 13*myquo +a[myrem] od: for k from 1 to 200 do printf(`%a,`,a[k]) od: # James Sellers, May 29 2000
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Mathematica
Set[#, {1, 3, 4, 6, 8, 9, 11, 12}] &@ Map[a[#] &, Range[0, 7]]; a[n_] := a[n] = 13 #1 + a[#2] & @@ QuotientRemainder[n, 8]; Array[a, 68, 0] (* Michael De Vlieger, Sep 08 2017 *) -
PARI
a(n) = floor((13*n - 1)/8); \\ Jon E. Schoenfield, Aug 21 2022
Formula
a(n) = floor((13*n - 1)/8). - Jon E. Schoenfield, Aug 21 2022
a(Fibonacci(n)-1) = Fibonacci(n+1) - 2, for n>=6 (Peters, 1981). - Amiram Eldar, Jan 27 2022
Extensions
More terms from James Sellers, May 29 2000