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A213183 Initialize a(1)=R=1. Repeat: copy the last R preceding terms to current position; increment R; do twice: append the least integer that has not appeared in the sequence yet. 1
1, 1, 2, 3, 2, 3, 4, 5, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Every positive integer k occurs floor((k+3)/2) times: 1 and 2 occur twice, 3 and 4 thrice, 5 and 6 four times, and so on.

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

a(1) = 1  -- initial value

a(2) = 1  -- copied one last term

a(3)=2, a(4)=3  -- appended two terms

a(5)=2, a(6)=3  -- copied two last terms

a(7)=4, a(8)=5  -- appended two terms

a(9)=3, a(10)=4, a(11)=5  -- copied three last terms

a(12)=6, a(13)=7  -- appended two terms

a(14)=4, a(15)=5, a(16)=6, a(17)=7  -- copied four last terms

a(18)=8, a(19)=9  -- appended two terms, and so on.

Comments from N. J. A. Sloane, Apr 28 2020, following a suggestion from Paul Curtz: (Start)

With an initial -1, 0, this may also be regarded as a triangle read by rows:

  -1;

   0,  1;

   1,  2,  3;

   2,  3,  4,  5;

   3,  4,  5,  6,  7;

   4,  5,  6,  7,  8,  9;

   5,  6,  7,  8,  9, 10, 11;

   6,  7,  8,  9, 10, 11, 12, 13;

  ...

or as an array read by upward antidiagonals:

  -1,  1,  3,  5,  7,  9, 11, ...

   0,  2,  4,  6,  8, 10, ...

   1,  3,  5,  7,  9, ...

   2,  4,  6,  8, ...

   3,  5,  7, ...

   4,  6, ...

   5, ...

  ...

(End)

PROG

(Python)

a = [1]*992

R = 1

i = 2

while i<900:

        for t in range(R):

                a[i] = a[i-R]

                i += 1

        R += 1

        a[i] = a[i-1] + 1

        i += 1

        a[i] = a[i-1] + 1

        i += 1

for i in range(1, 99):

        print(a[i], end=', ')

CROSSREFS

If we prefix this with -1, 0, and then add 1 to every term, we get A051162.

Sequence in context: A324532 A324390 A260112 * A125929 A309236 A071933

Adjacent sequences:  A213180 A213181 A213182 * A213184 A213185 A213186

KEYWORD

nonn,easy,tabf

AUTHOR

Alex Ratushnyak, Mar 05 2013

STATUS

approved

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)