A184220 a(n) = largest k such that A000290(n+1) = A000290(n) + (A000290(n) mod k), or 0 if no such k exists.

0, 0, 0, 0, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322, 359, 398, 439, 482, 527, 574, 623, 674, 727, 782, 839, 898, 959, 1022, 1087, 1154, 1223, 1294, 1367, 1442, 1519, 1598, 1679, 1762

Offset: 1

Author

Rémi Eismann, Jan 10 2011

Keywords

• nonn
• easy

Comments

From the definition, a(n) = A000290(n) - A005408(n) if A000217(n) - A005408(n) > A005408(n), 0 otherwise, where A000290 are the squares and A005408 are the gaps between squares: 2n + 1.

Examples

			For n = 3 we have A000290(3) = 9, A000290(4) = 16; there is no k such that 16 - 9 = 7 = (9 mod k), hence a(3) = 0.
For n = 5 we have A000290(5) = 25, A000290(6) = 36; 14 is the largest k such that 36 - 25 = 11 = (25 mod k), hence a(5) = 14; a(5) = A000290(5) - A005408(5) = 25 - 11 = 14.
For n = 25 we have A000217(25) = 625, A000217(26) = 676; 574 is the largest k such that 676 - 625 = 51 = (625 mod k), hence a(25) = 574; a(25) = A000290(25) - A005408(25) = 574.
		

Links

• Rémi Eismann, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Crossrefs

Cf. essentially the same as A008865, A000290, A005408, A133150, A184221, A118534, A117078, A117563, A001223.

Formula

a(n) = (n-1)^2-2 = A008865(n-1) for n >= 5 and a(n) = 0 for n <= 4.