A199408 - OEIS

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A199408

Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.

1, 2, 2, 3, 4, 3, 4, 4, 6, 4, 5, 6, 7, 8, 5, 6, 6, 6, 8, 10, 6, 7, 8, 9, 10, 11, 12, 7, 8, 8, 10, 8, 12, 12, 14, 8, 9, 10, 9, 12, 13, 12, 15, 16, 9, 10, 10, 12, 12, 10, 14, 16, 16, 18, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 11, 12, 12, 12, 12, 16, 12

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

OFFSET

1,2

COMMENTS

A diagonal of an n by k rectangle drawn on a square grid passes through T(n,k) squares: the diagonal enters n squares crossing horizontal segments and enters k squares crossing vertical segments. Gcd(n,k) counts the squares entered at a lattice point, which have been over-counted.

REFERENCES

M. Ollerton, Mathematics Teacher's Handbook, Continuum, 2009, pp. 14-15.

LINKS

Seiichi Manyama, Rows n = 1..140, flattened

Association of Teachers of Mathematics, Points of Departure 1, Derby, 1972.

FORMULA

T(d*a,d*b) = d*T(a,b).

EXAMPLE

T(6,4) = 6 + 4 - 2 = 8.

Triangular array begins

2 2

3 4 3

4 4 6 4

5 6 7 8 5

6 6 6 8 10 6

7 8 9 10 11 12 7

8 8 10 8 12 12 14 8

PROG

(PARI) T(n, k) = n + k - gcd(n, k); \\ Michel Marcus, Aug 04 2018

CROSSREFS

Cf. A049627, A074712. Third column A061800.

Sequence in context: A061295 A081742 A127432 * A285325 A135529 A061282

Adjacent sequences: A199405 A199406 A199407 * A199409 A199410 A199411

KEYWORD

nonn,tabl,easy

AUTHOR

Brian Hopkins, Nov 05 2011

STATUS

approved