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

0,3

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

Links

Table of n, a(n) for n=0..25.

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A061418 A355909 A136423 * A078932 A206740 A172161

Adjacent sequences: A215242 A215243 A215244 * A215246 A215247 A215248

Keyword

nonn,more,base

Author

N. J. A. Sloane, Aug 07 2012

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

Status

approved