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a(n) is the number m such that A242094(m) = A001950(n).
(Formerly M1330)
3

%I M1330 #30 Dec 26 2021 20:41:41

%S 2,5,7,9,12,14,17,19,21,24,26,28,31,33,36,38,40,43,45,47,49,51,54,56,

%T 58,61,63,66,68,70,73,75,77,80,82,85,87,89,92,94,97,99,101,104,106,

%U 108,111,113,116,118,120,123,125,127,129,131,134,136,138,141,143

%N a(n) is the number m such that A242094(m) = A001950(n).

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

%C Ron Reble remarks that Carlitz has a typo on page 339: Carlitz writes "In particular since (b) is a proper subset of (a), there exists a function v such that b = av." It should be "(b) is a proper subset of (u), ... b = uv." - _N. J. A. Sloane_, Jan 20 2020

%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.

%F a(n) = A001950(n) - j, where j is the largest integer such that A003234(j) < n. [Carlitz, Thm. 7.3]. - _Eric M. Schmidt_, Sep 16 2014

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a003256 = (+ 1) . fromJust . (`elemIndex` a242094_list) . a001950

%o -- _Reinhard Zumkeller_, Oct 03 2014

%Y Cf. A001950, A003234, A242094.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E New definition by _Eric M. Schmidt_, Aug 17 2014