A003249 -id:A003249

Search: a003249 -id:a003249

Displaying 1-5 of 5 results found.

page 1

A242094

Complement of A003249.

+20
7

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This is the function named u in [Carlitz].

First differs from A187947 at a(46)=51.

LINKS

Table of n, a(n) for n=1..67.

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

MATHEMATICA

nmax = 80;

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

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

A003234 = Select[Range[4*nmax],

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

A003249[n_] := A001950[A003234[[n]]] + 1;

Complement[Range[A003249[nmax]], Array[A003249, nmax]] (* Jean-François Alcover, Jul 21 2024 *)

PROG

(Haskell)

a242094 n = a242094_list !! (n-1)

a242094_list = c [1..] a003249_list where

c (v:vs) ws'@(w:ws) = if v == w then c vs ws else v : c vs ws'

-- Reinhard Zumkeller, Oct 03 2014

CROSSREFS

Cf. A003249.

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Aug 14 2014

STATUS

approved

A247427

2n - m, where m is the largest integer such that A003249(m) <= n.

+20
2

2, 4, 6, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 50, 52, 54, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 92, 94, 95, 97, 99, 101, 103, 104, 106, 108, 110, 112, 114, 116, 118, 119

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This is the function named sigma in [Carlitz] (cf. Thm. 7.2).

LINKS

Table of n, a(n) for n=1..63.

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

FORMULA

Definition of [Carlitz]: a(n) = A003254(A003247(n)).

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Sep 17 2014

STATUS

approved

A247424

Odd numbers not of the form 2*A005206(A003249(m)) - 1.

+20
1

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 49, 53, 55, 57, 59, 63, 65, 69, 71, 73, 75, 79, 81, 83, 85, 87, 89, 91, 95, 97, 99, 101, 105, 107, 109, 111, 113, 115, 117, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This is the function named y' in [Carlitz] (cf. proof of Thm. 7.31), which defines it as the complement of A247423.

LINKS

Table of n, a(n) for n=1..61.

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

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Sep 16 2014

STATUS

approved

A247429

A247427(n) for n in A003249; A247427(n) - 1 for other n.

+20
1

1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 51, 53, 55, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 83, 85, 87, 89, 91, 93, 95, 96, 98, 100, 102, 104, 105, 107, 109, 111, 113, 115, 117, 119

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This is the function named tau in [Carlitz].

LINKS

Table of n, a(n) for n=1..63.

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

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Sep 17 2014

STATUS

approved

A003252

The number m such that A003251(m) = A003231(n).
(Formerly M2521)

+10
1

3, 6, 9, 12, 15, 18, 21, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 61, 64, 67, 70, 73, 76, 79, 82, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 122, 125, 128, 131, 134, 137, 140, 143, 145, 148, 151, 154, 157, 159, 162, 165, 168, 171

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..59.

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

FORMULA

a(n) = 3n - j(n), where j(n) is the maximum number such that j(n) <= A003249(n). [Carlitz, Theorem 7.15.] - Eric M. Schmidt, Aug 17 2014

CROSSREFS

Cf. A003253.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Sequence corrected and extended by, and definition from Eric M. Schmidt, Aug 17 2014

STATUS

approved

page 1

Search completed in 0.008 seconds