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

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

Offset: 1

Author

Amarnath Murthy, Nov 14 2002

Keywords

• nonn
• tabl
• look

Comments

A260910 gives the triangle of Frobenius numbers of n, T(n,k). - Reinhard Zumkeller, Aug 04 2015

Examples

			Triangle begins:
  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;
  ...
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A077665, A077666.

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

Programs

Haskell

a077664 n k = a077664_tabl !! (n-1) !! (k-1)
a077664_row n = a077664_tabl !! (n-1)
a077664_tabl = map (\x -> take x $ filter ((== 1). gcd x) [x + 1 ..]) [1..]
-- Reinhard Zumkeller, Aug 03 2015

Mathematica

T[n_] := Module[{j, k}, Reap[For[j = n+1; k = 1, k <= n, j++, If[CoprimeQ[n, j], Sow[j]; k++]]][[2, 1]]];
Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Sep 21 2021 *)

Python

from math import gcd
def arow(n):
    rown, k = [], n + 1
    while len(rown) < n:
        if gcd(k, n) == 1: rown.append(k)
        k += 1
    return rown
def agen(rows):
    for n in range(1, rows+1): yield from arow(n)
print([an for an in agen(12)]) # Michael S. Branicky, Sep 21 2021

Extensions

More terms from Sascha Kurz, Jan 03 2003