A060470 Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j<k<n is two or less.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 19, 24, 26, 28, 33, 35, 37, 42, 44, 46, 51, 53, 55, 60, 62, 64, 69, 71, 73, 78, 80, 82, 87, 89, 91, 96, 98, 100, 105, 107, 109, 114, 116, 118, 123, 125, 127, 132, 134, 136, 141, 143, 145, 150, 152, 154, 159, 161, 163, 168, 170

Offset

1,2

Comments

Numbers {1,6,8} mod 9 plus {2,3,4,5,12}.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

From Chai Wah Wu, Feb 21 2018: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 13.

G.f.: x*(2*x^12 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1)/(x^4 - x^3 - x + 1). (End)

a(n) = 2*n + 3*floor(n/3 + 2/3) - 17 for n>9. - Bruno Berselli, Feb 22 2018

Example

12 is in the sequence since it is 4+8 and 2+10 but no other sum of two distinct terms.

Mathematica

f[s_List, j_Integer] := Block[{cnt, k = s[[-1]] + 1, ss = Plus @@@ Subsets[s, {j}]}, While[ cnt = Count[ss, k]; cnt == 0 || cnt > 2, k++]; Append[s, k]]; Nest[f[#, 2] &, {1, 2}, 70] (* Robert G. Wilson v, Jul 05 2014 *)
CoefficientList[Series[(2 x^12 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1) / (x^4 - x^3 - x + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Feb 22 2018 *)

Prog

(Magma) I:=[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 19, 24]; [n le 13 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Feb 22 2018
(Magma) [n le 9 select Floor(n^2/12+n/2+3/4) else 2*n+3*Floor(n/3+2/3)-17: n in [1..65]]; // Bruno Berselli, Feb 22 2018

Crossrefs

Cf. A003044, A033627, A060469, A060471, A060472. Virtually identical to A003663.

Sequence in context: A018478 A018350 A033058 * A003044 A279077 A018541

Adjacent sequences: A060467 A060468 A060469 * A060471 A060472 A060473

Keyword

nonn,easy

Author

Henry Bottomley, Mar 15 2001

Status

approved