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A184220 a(n) = largest k such that A000290(n+1) = A000290(n) + (A000290(n) mod k), or 0 if no such k exists. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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.

LINKS

Rémi Eismann, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

FORMULA

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

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A217837 A102876 A188166 * A026065 A010922 A010902

Adjacent sequences:  A184217 A184218 A184219 * A184221 A184222 A184223

KEYWORD

nonn,easy

AUTHOR

Rémi Eismann, Jan 10 2011

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.