A215245 a(n) = minimal value of A215244(k) for 2^n <= k < 2^(n+1).

1, 1, 2, 3, 4, 6, 9, 13, 20, 29, 42, 65, 95, 136, 212, 308, 444, 687, 1005, 1439, 2242, 3257, 4696, 7266, 10629, 15219

Offset: 0

Author

N. J. A. Sloane, Aug 07 2012

Keywords

• nonn
• more
• base

Comments

The initial terms roughly satisfy a(n) approx.= a(n-1)+a(n-3), which leads to the guess that perhaps a(n) ~ 1.4655^n, from the real zero of x^3-x-1. - N. J. A. Sloane, Aug 08 2012

Examples

			The values of A215244(k) for k=8 through 15 are (4, 3, 3, 3, 4, 3, 4, 8), with minimal value a(3) = 3.
		

Links

• Giovanni Resta, Examples of words attaining the minimal value for n = 0..25

Crossrefs

Cf. A215244, A215246, A215253, A215254. A215255 gives an upper bound.

Programs

Maple

A215245 := proc(n)
    local a,k ;
    a := A215244(2^n) ;
    for k from 2^n+1 to 2^(n+1)-1 do
        a := min(a,A215244(k)) ;
    end do:
    a ;
end proc: # R. J. Mathar, Aug 07 2012

Mathematica

palQ[L_] := SameQ[L, Reverse[L]];
b[L_] := b[L] = Module[{a = palQ[L] // Boole, c}, For[c = 1, c < Length[L], c++, If[palQ[L[[;; c]]], a = a + b[L[[c+1 ;;]]]]]; a];
a215244[n_] := If[n == 1, 1, b[IntegerDigits[n, 2]]];
a215245[n_] := Module[{a, k}, a = a215244[2^n]; For[k = 2^n+1, k <= 2^(n+1) - 1, k++, a = Min[a, a215244[k]]]; a];
a215245 /@ Range[0, 20] (* Jean-François Alcover, Oct 28 2019 *)

Extensions

a(10)-a(13) from R. J. Mathar, Aug 07 2012

a(14)-a(17) from N. J. A. Sloane, Aug 08 2012, using Mathar's Maple code.

a(18)-a(25) from Giovanni Resta, Mar 19 2013