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%I M2323 N0918 #40 Sep 04 2022 13:20:24
%S 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,
%T 42,43,45,47,48,50,51,53,55,56,58,60,61,63,64,66,68,69,71,73,74,76,77,
%U 79,81,82,84,86,87,89,90,92,94,95,97,99,100,102,103,105,107,108,110
%N a(8i+j) = 13i + a(j), where 1<=j<=8.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Michael De Vlieger, <a href="/A000202/b000202.txt">Table of n, a(n) for n = 1..10000</a>
%H James F. Peters, <a href="https://fq.math.ca/Scanned/19-2/advanced19-2.pdf">Problem H-327</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 19, No. 2 (1981), p. 189; <a href="https://www.fq.math.ca/Scanned/20-4/advanced20-4.pdf">Are You Curious?</a>, Solution to Problem H-327 by Paul S. Bruckman, ibid., Vol. 20, No. 4 (1982), pp. 373-375.
%H D. E. Thoro, <a href="https://fq.math.ca/Scanned/1-2/advanced1-2.pdf">Problem H-12</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 1, No. 2 (1963), p. 54; <a href="https://www.fq.math.ca/Scanned/1-4/advanced1-4.pdf">A Curious Sequence</a>, Solution to Problem H-12 by Malcolm Tallman, ibid., Vol. 1, No. 4 (1963), p. 50.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).
%F a(n) = floor((13*n - 1)/8). - _Jon E. Schoenfield_, Aug 21 2022
%F a(Fibonacci(n)-1) = Fibonacci(n+1) - 2, for n>=6 (Peters, 1981). - _Amiram Eldar_, Jan 27 2022
%p 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 A. Sellers_, May 29 2000
%t 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 *)
%o (PARI) a(n) = floor((13*n - 1)/8); \\ _Jon E. Schoenfield_, Aug 21 2022
%Y Different from A000201, A066096, A090908.
%Y Cf. A000045.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, May 29 2000
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