A066790 a(n) = least natural number k such that the distance between (n, sigma(n)) and (n+k, sigma(n+k)) is an integer (i.e., k^2 + (sigma(n+k) - sigma(n))^2 is a square), if such k exists; 0 otherwise.

113520, 8, 99585, 44, 5, 5, 48, 10, 280, 3, 45, 3, 2808, 1, 6, 9, 16, 4, 66, 6, 6, 133, 10, 9, 11, 14, 6, 11, 11, 16, 45, 1188, 2, 19, 12, 448, 56, 9, 12, 5, 8, 20, 102, 21, 24, 5, 72, 15, 4, 104, 4, 6, 288, 2, 7, 10, 12, 31, 35, 10, 165, 7, 6, 105, 13, 4, 138, 14, 8, 15, 72, 392

Offset

1,1

Comments

Is a(n) nonzero for all n?

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

8^2 + (sigma(2 + 8) - sigma(2))^2 = 17^2 and k = 8 is the least natural number achieving this, so a(2) = 8.

Prog

(PARI) { for (n=1, 1000, s=sigma(n); k=0; b=0; while(b==0, k++; if (issquare(k^2 + (sigma(n+k) - s)^2), b=1)); write("b066790.txt", n, " ", k) ) } \\ Harry J. Smith, Mar 26 2010

Crossrefs

Sequence in context: A259010 A259003 A256901 * A135411 A108387 A112009

Adjacent sequences: A066787 A066788 A066789 * A066791 A066792 A066793

Keyword

nonn

Author

Joseph L. Pe, Jan 18 2002

Extensions

Terms a(51) - a(72) from Harry J. Smith, Mar 26 2010

Status

approved