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, 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

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: A324390 A260112 A361838 * A125929 A309236 A071933

Adjacent sequences: A213180 A213181 A213182 * A213184 A213185 A213186

Keyword

nonn,easy,tabf

Author

Alex Ratushnyak, Mar 05 2013

Status

approved