A060471 Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j<k<n is three or less.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 21, 23, 25, 30, 32, 34, 36, 41, 43, 45, 47, 52, 54, 56, 58, 63, 65, 67, 69, 74, 76, 78, 80, 85, 87, 89, 91, 96, 98, 100, 102, 107, 109, 111, 113, 118, 120, 122, 124, 129, 131, 133, 135, 140, 142, 144, 146, 151, 153, 155, 157

Offset

1,2

Comments

Numbers {1,3,8,10} mod 11 plus {2,4,5,6,7,16}. Note that while the cases for "zero", "one", "two" and "four" essentially involve a third of the natural numbers, this case for "three" involves 4/11.

Links

Table of n, a(n) for n=1..64.

Formula

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 17.

G.f.: x*(2*x^16 + x^12 + x^11 + x^10 + x^9 + x^8 + x^3 + x^2 + x + 1)/(x^5 - x^4 - x + 1). (End)

Example

12 is in the sequence since it is 5+7, 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 > 3, k++]; Append[s, k]]; Nest[f[#, 2] &, {1, 2}, 70] (* Robert G. Wilson v, Jul 05 2014 *)

Crossrefs

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

Sequence in context: A141340 A182419 A033060 * A003045 A279079 A029750

Adjacent sequences: A060468 A060469 A060470 * A060472 A060473 A060474

Keyword

nonn

Author

Henry Bottomley, Mar 15 2001

Status

approved