A060442 Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), without repetition.

0, 1, 1, 2, 3, 5, 2, 13, 3, 7, 2, 17, 5, 11, 89, 2, 3, 233, 13, 29, 2, 5, 61, 3, 7, 47, 1597, 2, 17, 19, 37, 113, 3, 5, 11, 41, 2, 13, 421, 89, 199, 28657, 2, 3, 7, 23, 5, 3001, 233, 521, 2, 17, 53, 109, 3, 13, 29, 281, 514229, 2, 5, 11, 31, 61, 557, 2417, 3, 7, 47, 2207, 2, 89

Offset: 0

Author

N. J. A. Sloane, Apr 07 2001

Keywords

• nonn
• tabf
• easy

Comments

Rows have irregular lengths.

T(n,k) = A027748(A000045(n),k), k = 1 .. A022307(n). - Reinhard Zumkeller, Aug 30 2014

Examples

			Triangle begins:
     0;
     1;
     1;
     2;
     3;
     5;
     2;
    13;
     3,   7;
     2,  17;
     5,  11;
    89;
     2,   3;
   233;
    13,  29;
     2,   5, 61;
     3,   7, 47;
  1597;
     2,  17, 19;
    37, 113;
     3,   5, 11, 41;
   ...
		

Links

• T. D. Noe and Charles R Greathouse IV, Rows n=0..1422 of triangle, flattened (rows up to 1000 from Noe; using existing factorization databases)
• J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
• Blair Kelly, Fibonacci and Lucas Factorizations

Crossrefs

Cf. A000045, A060441.

Cf. A027748, A022307 (row lengths for n>2), A001221.

Programs

Haskell

a060442 n k = a060442_tabf !! n !! k
a060442_row n = a060442_tabf !! n
a060442_tabf = [0] : [1] : [1] : map a027748_row (drop 3 a000045_list)
-- Reinhard Zumkeller, Aug 30 2014

Maple

with(numtheory): with(combinat): for i from 3 to 50 do for j from 1 to nops(ifactors(fibonacci(i))[2]) do printf(`%d,`, ifactors(fibonacci(i))[2][j][1]) od: od:

Extensions

More terms from James Sellers, Apr 09 2001