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%I #3 Mar 31 2012 10:28:53
%S 1,2,1,3,3,2,5,6,5,2,7,11,11,7,4,11,18,22,18,11,2,13,29,40,40,29,13,6,
%T 17,42,69,80,69,42,19,4,19,59,111,149,149,111,61,23,6,23,78,170,260,
%U 298,260,172,84,29,4,29,101,248,430,558,558,432,256,113,33,10
%N Triangle read by rows: prime numbers p(n) along left edge (n, 1) and totient phi(n) along right edge (n, n), with (n, k) = (n - 1, k - 1) + (n - 1, k) for 1 < k < n when n > 2.
%C (1, 1) = 1 is considered a member of both sequences.
%C If (n, n - 1) is a prime p, n is less than or equal to the index of p (A049084(p) + 1) and strictly less if n >= 8: (8, 7) = 19 and (9, 1) = 19.
%C If (n, k) is a prime p, with n > 3 and 1 < k < n - 1, then n < A049084(p) + 1: (5, 2) = (5, 3) = 11 and (6, 1) = 11.
%C Excluding the right edge, the triangle has deteriorating symmetry about its midline until n = 12: (12, 5) = 988 and (12, 7) = 990.
%C The diamond of symmetry ends with (11, 5) = (11, 6) = 558 and coincidentally 11 is the last row which could be entered.
%C There is a related triangle which begins with p(1) = 2 and phi(1) = 1 on the first row, omitting the peak:
%C 2 1
%C 3 3 1
%C 5 6 4 2
%C 7 11 10 6 2
%C 11 18 21 16 8 4
%C It appears to have less interesting properties.
%Y Cf. A000040, A000010
%K easy,nonn,tabl
%O 1,2
%A _Reikku Kulon_, Sep 17 2008
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