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A000202
a(8i+j) = 13i + a(j), where 1<=j<=8.
(Formerly M2323 N0918)
1
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
1,2
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
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.
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
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 A. Sellers, May 29 2000
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 *)
PROG
(PARI) a(n) = floor((13*n - 1)/8); \\ Jon E. Schoenfield, Aug 21 2022
CROSSREFS
Different from A000201, A066096, A090908.
Cf. A000045.
Sequence in context: A000201 A090908 A292644 * A188035 A026339 A182774
KEYWORD
nonn,easy
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved