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A077664 Triangle in which the n-th row contains n smallest numbers greater than n and coprime to n.

%I A077664 #17 Sep 21 2021 19:55:21
%S A077664 2,3,5,4,5,7,5,7,9,11,6,7,8,9,11,7,11,13,17,19,23,8,9,10,11,12,13,15,
%T A077664 9,11,13,15,17,19,21,23,10,11,13,14,16,17,19,20,22,11,13,17,19,21,23,
%U A077664 27,29,31,33,12,13,14,15,16,17,18,19,20,21,23,13,17,19,23,25,29,31,35,37,41,43,47
%N A077664 Triangle in which the n-th row contains n smallest numbers greater than n and coprime to n.
%C A077664 A260910 gives the triangle of Frobenius numbers of n, T(n,k). - _Reinhard Zumkeller_, Aug 04 2015
%H A077664 Reinhard Zumkeller, <a href="/A077664/b077664.txt">Rows n = 1..125 of triangle, flattened</a>
%e A077664 Triangle begins:
%e A077664   2;
%e A077664   3,  5;
%e A077664   4,  5,  7;
%e A077664   5,  7,  9, 11;
%e A077664   6,  7,  8,  9, 11;
%e A077664   7, 11, 13, 17, 19, 23;
%e A077664   8,  9, 10, 11, 12, 13, 15;
%e A077664   ...
%t A077664 T[n_] := Module[{j, k}, Reap[For[j = n+1; k = 1, k <= n, j++, If[CoprimeQ[n, j], Sow[j]; k++]]][[2, 1]]];
%t A077664 Table[T[n], {n, 1, 12}] // Flatten (* _Jean-François Alcover_, Sep 21 2021 *)
%o A077664 (Haskell)
%o A077664 a077664 n k = a077664_tabl !! (n-1) !! (k-1)
%o A077664 a077664_row n = a077664_tabl !! (n-1)
%o A077664 a077664_tabl = map (\x -> take x $ filter ((== 1). gcd x) [x + 1 ..]) [1..]
%o A077664 -- _Reinhard Zumkeller_, Aug 03 2015
%o A077664 (Python)
%o A077664 from math import gcd
%o A077664 def arow(n):
%o A077664     rown, k = [], n + 1
%o A077664     while len(rown) < n:
%o A077664         if gcd(k, n) == 1: rown.append(k)
%o A077664         k += 1
%o A077664     return rown
%o A077664 def agen(rows):
%o A077664     for n in range(1, rows+1): yield from arow(n)
%o A077664 print([an for an in agen(12)]) # _Michael S. Branicky_, Sep 21 2021
%Y A077664 Cf. A077665, A077666.
%Y A077664 Cf. A077581, A260895 (number of primes per row), A260910.
%K A077664 nonn,tabl,look
%O A077664 1,1
%A A077664 _Amarnath Murthy_, Nov 14 2002
%E A077664 More terms from _Sascha Kurz_, Jan 03 2003