A121325 Juxtaposition of the prime factors of 4*n^2 + 1 with multiplicity.

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

For n=4, 4n^2+1 = 65 = 5*13. 5 and 13 are the 4th and 5th entries.

Mathematica

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

Prog

(PARI) fourxsqp1 (n)= { forstep(x=1, n, 1, y=4*x^2+1; a=ifactor(y); for(j=1, length(a), print1(a[j]", ") ) ) } ifactor(n) = \The vector of the integer factors of n with multiplicity. { 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) }

Crossrefs

Sequence in context: A186029 A083048 A123669 * A256970 A145689 A321658

Adjacent sequences: A121322 A121323 A121324 * A121326 A121327 A121328

Keyword

nonn

Author

Cino Hilliard, Aug 26 2006

Status

approved