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

0,4

Comments

Rows have irregular lengths.

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

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

Example

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;
   ...

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:

Prog

(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

Crossrefs

Cf. A000045, A060441.

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

Sequence in context: A102867 A060383 A139044 * A060385 A080648 A113195

Adjacent sequences: A060439 A060440 A060441 * A060443 A060444 A060445

Keyword

nonn,tabf,easy

Author

N. J. A. Sloane, Apr 07 2001

Extensions

More terms from James A. Sellers, Apr 09 2001

Status

approved