A246399 Least k such that A249783(k) = n.

1, 4, 7, 12, 17, 22, 27, 43, 51, 59, 67, 75, 83, 122, 135, 148, 161, 174, 187, 200, 213, 226, 239, 344, 365, 386, 407, 428, 449, 470, 491, 512, 533, 554, 575, 596, 617, 638, 659, 931, 965, 999, 1033, 1067, 1101, 1135, 1169, 1203, 1237, 1271

Offset: 1

Author

Charles R Greathouse IV, Nov 13 2014

Keywords

• nonn

Comments

It appears that a(n) exists for each n, and that the sequence is increasing.

Examples

			a(3) = 7 because the Fibonacci-like sequence 2, 1, 3, 4, 7, 11, ... contains 7 and the sum of the first two terms is 3, while no smaller sequences work. (All terms must be nonnegative.)
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• Index to sequences related to the complexity of n

Crossrefs

Cf. A249783, A054495.

Programs

Mathematica

A249783[n_] := A249783[n] = Module[{a, k, A, B}, If[n<2, Return[n]]; For[k = 1, k <= n-1, k++, For[a=0, a <= k-1, a++, A = a; B = k-A; While[BA249783[k] == n, Return[k]]]; Array[a, 50] (* Jean-François Alcover, Jan 06 2017, adapted from PARI *)

PARI

A054495(n)=fordiv(n,d,if(A010056(n/d),return(d)))
A249783(n)=if(n<2,return(n));for(k=1,n-1,for(a=0,k-1,my(A=a,B=k-A);while(B=least&&t<=#v&&v[t]==0,v[t]=n;while(v[least],if(least++>#v,return(v)))))