A003249 - OEIS

%I M4492 #29 Jul 21 2024 12:47:59

%S 8,21,29,42,50,55,63,76,84,97,110,118,131,139,144,152,165,173,186,194,

%T 199,207,220,228,241,254,262,275,283,288,296,309,317,330,338,343,351,

%U 364,372,377,385,398,406,419,427,432,440,453,461,474,487,495,508,516

%N a(n) = A001950(A003234(n)) + 1.

%C This is the function named u' in [Carlitz]. - _Eric M. Schmidt_, Aug 14 2014

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H L. Carlitz, R. Scoville and T. Vaughan, <a href="http://www.fq.math.ca/Scanned/11-4/carlitz.pdf">Some arithmetic functions related to Fibonacci numbers</a>, Fib. Quart., 11 (1973), 337-386.

%p A003249 := proc(n)

%p     A001950(A003234(n)) +1 ;

%p end proc:

%p seq(A003249(n),n=1..80) ; # _R. J. Mathar_, Jul 16 2024

%t nmax = 80;

%t A001950[n_] := Floor[n*GoldenRatio^2];

%t A003231[n_] := 2*n + Floor[n*GoldenRatio];

%t A003234 = Select[Range[4*nmax],

%t    A003231[A001950[#]] == A001950[A003231[#]] - 1&];

%t a[n_] := A001950[A003234[[n]]] + 1;

%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Jul 21 2024 *)

%o (Haskell)

%o a003249 = (+ 1) . a001950 . a003234 -- _Reinhard Zumkeller_, Oct 03 2014

%Y Cf. A242094 (complement), A001950, A003234.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E Corrected and extended by, and a definition from _Eric M. Schmidt_, Aug 14 2014