A060469 Smallest positive a(n) such that number of solutions to a(n) = a(j)+a(k) j<k<n is one or less.

1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 23, 25, 28, 30, 35, 37, 40, 42, 47, 49, 52, 54, 59, 61, 64, 66, 71, 73, 76, 78, 83, 85, 88, 90, 95, 97, 100, 102, 107, 109, 112, 114, 119, 121, 124, 126, 131, 133, 136, 138, 143, 145, 148, 150, 155, 157, 160, 162, 167, 169, 172, 174

Offset

1,2

Comments

Numbers {1,4,6,11} mod 12 plus {2,3,8}.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = a(n-1)+a(n-4)-a(n-5) for n>9. - Colin Barker, Feb 27 2015

G.f.: x*(2*x^10+x^8+x^7+2*x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Feb 27 2015

Example

11 is in the sequence since it is 3+8 but no other sum of two distinct terms.

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 23}, 100] (* Paolo Xausa, Mar 04 2024 *)

Prog

(PARI) Vec(x*(2*x^10+x^8+x^7+2*x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)^2*(x+1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Feb 27 2015

Crossrefs

Cf. A002858, A033627, A060469, A060470, A060471, A060472.

Virtually identical to A003662.

Sequence in context: A023024 A018362 A033056 * A080329 A002858 A211522

Adjacent sequences: A060466 A060467 A060468 * A060470 A060471 A060472

Keyword

nonn,easy

Author

Henry Bottomley, Mar 15 2001

Status

approved