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a(n) = n + 2*ceiling(phi n), where phi = (1 + sqrt(5))/2. Row 1 of A101866.
6

%I #16 Mar 20 2024 09:35:12

%S 5,10,13,18,23,26,31,34,39,44,47,52,57,60,65,68,73,78,81,86,89,94,99,

%T 102,107,112,115,120,123,128,133,136,141,146,149,154,157,162,167,170,

%U 175,178,183,188,191,196,201,204,209,212,217,222,225,230,233,238,243,246,251,256

%N a(n) = n + 2*ceiling(phi n), where phi = (1 + sqrt(5))/2. Row 1 of A101866.

%C Positions of 1 in A188009 = (0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,...)

%C A101868 = (5, 10, 13, 18, 23, 26, 31, 34, 39, 44, 47, 52, 57, 60, ...). - Clark Kimberling, Mar 19 2011, corrected by _M. F. Hasler_, Oct 12 2017

%C Essentially the same as A188434, which has an initial 2 prefixed. However, the present sequence would have a(0) = 0 if extended to offset / index 0. - _M. F. Hasler_, Oct 12 2017

%H Paolo Xausa, <a href="/A101868/b101868.txt">Table of n, a(n) for n = 1..10000</a>

%t Array[# + 2*Ceiling[#*GoldenRatio] &, 100] (* _Paolo Xausa_, Mar 20 2024 *)

%o (PARI) a(n)=n+2*ceil(quadgen(5)*n+.) \\ _M. F. Hasler_, Oct 12 2017

%Y Cf. A188009, A101868, A188434.

%Y Cf. A001622, A101866.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jan 28 2005