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A060471 Smallest positive a(n) such that number of solutions to a(n)=a(j)+a(k) j<k<n is three or less. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)