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A276574 The infinite trunk of least squares beanstalk with reversed subsections. 7
0, 3, 8, 6, 15, 11, 24, 21, 18, 16, 35, 32, 30, 27, 48, 45, 43, 40, 38, 63, 59, 56, 53, 51, 80, 78, 75, 72, 70, 67, 64, 99, 96, 93, 90, 88, 85, 83, 120, 117, 115, 112, 108, 105, 102, 143, 139, 136, 134, 131, 128, 126, 123, 168, 165, 162, 160, 158, 155, 152, 149, 147, 144, 195, 192, 189, 186, 183, 179, 176, 173, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10028

FORMULA

a(0) = 0; a(1) = 3; for n > 1, let k = A255131(a(n-1)). If k+1 is not a square, then a(n) = k, otherwise a(n) = A000290(2+A000196(k+1)) - 1.

EXAMPLE

This can be viewed as an irregular table, where after 0, each row has A260734(n) = 1, 2, 2, 4, 4, 5, 5, 7, ... terms:

0;

3;

8, 6;

15, 11;

24, 21, 18, 16;

35, 32, 30, 27;

48, 45, 43, 40, 38;

63, 59, 56, 53, 51;

80, 78, 75, 72, 70, 67, 64;

99, 96, 93, 90, 88, 85, 83;

120, 117, 115, 112, 108, 105, 102;

...

Each row begins with (n^2)-1 (see A005563), and each successive term is obtained by subtracting A002828(k) from the previous term k, until ((n-1)^2)-1 would be encountered, which is not listed second time (as it already occurs as the first term of the previous row), but instead, the current row is finished and the next row is started with the term ((n+1)^2)-1.

PROG

(Scheme)

(definec (A276574 n) (cond ((zero? n) n) ((= 1 n) 3) (else (let ((maybe_next (A255131 (A276574 (- n 1))))) (if (zero? (A010052 (+ 1 maybe_next))) maybe_next (+ -1 (A000290 (+ 2 (A000196 (+ 1 maybe_next))))))))))

CROSSREFS

Cf. A005563 (left edge), A277023 (right edge).

Cf. A000196, A000290, A002828, A010052, A255131, A260734, A262689, A276572.

Used to construct A276573.

Cf. A277015 (tells which rows end with squares, listed in A277016).

Sequence in context: A289485 A304299 A221951 * A276584 A098737 A164654

Adjacent sequences:  A276571 A276572 A276573 * A276575 A276576 A276577

KEYWORD

nonn,tabf

AUTHOR

Antti Karttunen, Sep 07 2016

EXTENSIONS

Example section added and the formula rewritten to a simpler form (which is now correct) - Antti Karttunen, Oct 16 2016

STATUS

approved

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Last modified April 14 06:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)