A077664 - OEIS

%I #17 Sep 21 2021 19:55:21

%S 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 9,11,13,15,17,19,21,23,10,11,13,14,16,17,19,20,22,11,13,17,19,21,23,

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

%C A260910 gives the triangle of Frobenius numbers of n, T(n,k). - _Reinhard Zumkeller_, Aug 04 2015

%H Reinhard Zumkeller, <a href="/A077664/b077664.txt">Rows n = 1..125 of triangle, flattened</a>

%e Triangle begins:

%e   2;

%e   3,  5;

%e   4,  5,  7;

%e   5,  7,  9, 11;

%e   6,  7,  8,  9, 11;

%e   7, 11, 13, 17, 19, 23;

%e   8,  9, 10, 11, 12, 13, 15;

%e   ...

%t 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 Table[T[n], {n, 1, 12}] // Flatten (* _Jean-François Alcover_, Sep 21 2021 *)

%o (Haskell)

%o a077664 n k = a077664_tabl !! (n-1) !! (k-1)

%o a077664_row n = a077664_tabl !! (n-1)

%o a077664_tabl = map (\x -> take x $ filter ((== 1). gcd x) [x + 1 ..]) [1..]

%o -- _Reinhard Zumkeller_, Aug 03 2015

%o (Python)

%o from math import gcd

%o def arow(n):

%o     rown, k = [], n + 1

%o     while len(rown) < n:

%o         if gcd(k, n) == 1: rown.append(k)

%o         k += 1

%o     return rown

%o def agen(rows):

%o     for n in range(1, rows+1): yield from arow(n)

%o print([an for an in agen(12)]) # _Michael S. Branicky_, Sep 21 2021

%Y Cf. A077665, A077666.

%Y Cf. A077581, A260895 (number of primes per row), A260910.

%K nonn,tabl,look

%O 1,1

%A _Amarnath Murthy_, Nov 14 2002

%E More terms from _Sascha Kurz_, Jan 03 2003