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

1,1

Comments

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

Links

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

Example

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;
  ...

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 *)

Prog

(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
(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

Crossrefs

Cf. A077665, A077666.

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

Sequence in context: A263279 A262507 A151679 * A329402 A339263 A179475

Adjacent sequences: A077661 A077662 A077663 * A077665 A077666 A077667

Keyword

nonn,tabl,look

Author

Amarnath Murthy, Nov 14 2002

Extensions

More terms from Sascha Kurz, Jan 03 2003

Status

approved