A121325 Irregular triangle read by rows in which the n-th row gives the prime factors of 4*n^2 + 1 with repetition.

5, 17, 37, 5, 13, 101, 5, 29, 197, 257, 5, 5, 13, 401, 5, 97, 577, 677, 5, 157, 17, 53, 5, 5, 41, 13, 89, 1297, 5, 17, 17, 1601, 5, 353, 13, 149, 29, 73, 5, 461, 41, 61, 5, 541, 2917, 3137, 5, 673, 13, 277, 5, 769, 17, 241, 4357, 5, 5, 5, 37, 13, 13, 29, 5, 17, 61, 5477, 53

Offset

1,1

Comments

These numbers are all of the form 4m+1.

Links

Table of n, a(n) for n=1..67.

Example

Triangle begins:
  5;
  17;
  37;
  5, 13;
  101;
  5, 29;
  197;
  257;
  5, 5, 13;
  401;
  5, 97;
  577;
  ...

Mathematica

Flatten[Table[Table[First[#], {Last[#]}]&/@FactorInteger[4*n^2+1], {n, 60}]]  (* Harvey P. Dale, Dec 19 2011 *)

Prog

(PARI) \\ here ifactor(n) gives n-th row of A027746.
ifactor(n) = { local(f, j, k, flist); flist=[]; f=Vec(factor(n)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }
row(n)= { ifactor(4*n^2+1) }

Crossrefs

Cf. A027746 (similar triangle for n).

Sequence in context: A186029 A083048 A123669 * A256970 A145689 A321658

Adjacent sequences: A121322 A121323 A121324 * A121326 A121327 A121328

Keyword

nonn,tabf

Author

Cino Hilliard, Aug 26 2006

Status

approved