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A005041 A self-generating sequence.
(Formerly M0258)
3
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A008620 for run lengths: each k occurs A008620(k+2) times. [Reinhard Zumkeller, Mar 16 2012]

REFERENCES

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

James Propp, Problem 1047, Math. Mag., 52 (1979), 265.

J. Shallit, Letter to N. J. A. Sloane, Nov 10 1979.  Attached: James Propp, Problem 1047, Math. Mag., 52 (1979), 265. [Annotated scanned copy]

Aaron Snook, Augmented Integer Linear Recurrences, Thesis, 2012. - From N. J. A. Sloane, Dec 19 2012

FORMULA

For any k in {0, 1, 2, ...} and r in {0, 1, 2), we have: if n=6*k+(3/2)*(k)*(k-1)+r*(k+2), then a(n)=3*k+r+1. E.g. for k=3 and r=1, we have n=6*3+(3/2)*(3)*(3-1)+1*(3+2)=32 and so a(32)=3*3+1+1=11. - Francois Jooste (phukraut(AT)hotmail.com), Mar 12 2002

MATHEMATICA

Table[n+1, {n, 0, 20}, {Ceiling[(n+1)/3]+1}] // Flatten (* Jean-Fran├žois Alcover, Dec 10 2014 *)

PROG

(Haskell)

a005041 n = a005041_list !! n

a005041_list = 1 : f 1 1 (tail ts) where

   f y i gs'@((j, a):gs) | i < j  = y : f y (i+1) gs'

                        | i == j = a : f a (i+1) gs

   ts = [(6*k + 3*k*(k-1) `div` 2 + r*(k+2), 3*k+r+1) |

         k <- [0..], r <- [0, 1, 2]]

-- Reinhard Zumkeller, Mar 16 2012

CROSSREFS

Cf. A005038, A005039, A005040, A005043, A005044, A055086, A001462, A082462, A024417, A084500.

Sequence in context: A001462 A082462 A276581 * A030530 A084500 A084557

Adjacent sequences:  A005038 A005039 A005040 * A005042 A005043 A005044

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Jeffrey Shallit

EXTENSIONS

More terms from Samuel Hilliard (sam_spade1977(AT)hotmail.com), Apr 11 2004

STATUS

approved

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Last modified June 24 01:22 EDT 2018. Contains 311819 sequences. (Running on oeis4.)