A003256 a(n) is the number m such that A242094(m) = A001950(n).

2, 5, 7, 9, 12, 14, 17, 19, 21, 24, 26, 28, 31, 33, 36, 38, 40, 43, 45, 47, 49, 51, 54, 56, 58, 61, 63, 66, 68, 70, 73, 75, 77, 80, 82, 85, 87, 89, 92, 94, 97, 99, 101, 104, 106, 108, 111, 113, 116, 118, 120, 123, 125, 127, 129, 131, 134, 136, 138, 141, 143

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This is the function named v in [Carlitz]. - Eric M. Schmidt, Aug 14 2014

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

References

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

Links

• L. Carlitz, R. Scoville and T. Vaughan, Some arithmetic functions related to Fibonacci numbers, Fib. Quart., 11 (1973), 337-386.

Crossrefs

Cf. A001950, A003234, A242094.

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a003256 = (+ 1) . fromJust . (`elemIndex` a242094_list) . a001950
-- Reinhard Zumkeller, Oct 03 2014

Formula

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

Extensions

New definition by Eric M. Schmidt, Aug 17 2014