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

1,2

Comments

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Index to sequences related to the complexity of n

Example

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.)

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

Prog

(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<n, [A, B]=[B, A+B]); if(B==n, return(k)))); n
v=vector(100); least=1; for(n=1, 1e7, if(aa(n)<least, next); t=a(n); if(t>=least&&t<=#v&&v[t]==0, v[t]=n; while(v[least], if(least++>#v, return(v)))))

Crossrefs

Cf. A249783, A054495.

Sequence in context: A310789 A310790 A310791 * A276222 A074148 A336660

Adjacent sequences: A246396 A246397 A246398 * A246400 A246401 A246402

Keyword

nonn

Author

Charles R Greathouse IV, Nov 13 2014

Status

approved