cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A199408 Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.

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%I A199408 #20 Aug 04 2018 10:36:03
%S A199408 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,
%T A199408 12,12,14,8,9,10,9,12,13,12,15,16,9,10,10,12,12,10,14,16,16,18,10,11,
%U A199408 12,13,14,15,16,17,18,19,20,11,12,12,12,12,16,12
%N A199408 Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.
%C A199408 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.
%D A199408 M. Ollerton, Mathematics Teacher's Handbook, Continuum, 2009, pp. 14-15.
%H A199408 Seiichi Manyama, <a href="/A199408/b199408.txt">Rows n = 1..140, flattened</a>
%H A199408 Association of Teachers of Mathematics, <a href="https://www.atm.org.uk/Shop/Points-of-Departure-1---PDF/dnl003">Points of Departure 1</a>, Derby, 1972.
%F A199408 T(d*a,d*b) = d*T(a,b).
%e A199408 T(6,4) = 6 + 4 - 2 = 8.
%e A199408 Triangular array begins
%e A199408   1
%e A199408   2  2
%e A199408   3  4  3
%e A199408   4  4  6  4
%e A199408   5  6  7  8  5
%e A199408   6  6  6  8 10  6
%e A199408   7  8  9 10 11 12  7
%e A199408   8  8 10  8 12 12 14  8
%o A199408 (PARI) T(n,k) = n + k - gcd(n,k); \\ _Michel Marcus_, Aug 04 2018
%Y A199408 Cf. A049627, A074712.  Third column A061800.
%K A199408 nonn,tabl,easy
%O A199408 1,2
%A A199408 _Brian Hopkins_, Nov 05 2011