A281131 First appearance of 2^n in A281130.

1, 3, 7, 13, 23, 41, 98, 223, 437, 699, 1213, 2624, 4674, 11163, 21300, 40858, 73977, 148591, 297394, 567076, 1100738, 2243474, 4340628, 8726122, 17397270, 34701556, 68372147, 136254352, 271069771, 546613630, 1088921640, 2163138108, 4334318825

Offset: 0

Author

Rok Cestnik, Jan 15 2017

Keywords

• nonn
• hard

Comments

Conjecture: a(n) ~ 2^n.

Examples

			a(1) = 3 because A281130(3) = 2^1 and A281130(i) != 2^1 for i < 3.
a(2) = 7 because A281130(7) = 2^2 and A281130(i) != 2^2 for i < 7.
		

Links

• Rok Cestnik, C program (utilizing hard drive memory)

Crossrefs

Cf. A281130, A291598.

Programs

C

#include
#include
int main(void){
   int N = 1000000000;
   int *a = (int*)malloc((N+1)*sizeof(int));
   int max = 1;
   int maxindex = 1;
   a[1] = 1;
   a[2] = 1;
   for(int i = 2; i < N; ++i){
      if(a[i-1] < a[i]) a[i+1] = a[i-a[i]];
      else a[i+1] = 2*a[i];
      if(a[i+1] > max){
         max = a[i+1];
         printf("%d %d\n", maxindex, i+1);
         maxindex++;
      }
   }
   return 0;
}

Mathematica

a[n_] := a[n] = If[a[n - 2] < a[n - 1], a[n - 1 - a[n - 1]], 2 a[n - 1]]; a[1] = a[2] = 1; Function[w, Function[e, First /@ Lookup[w, 2^e]]@ Range[0, Log2@ Max@ Keys@ w]]@ PositionIndex@ Array[a, 10^7] (* Michael De Vlieger, Jan 21 2017, Version 10. *)

Extensions

a(31)-a(32) from Rok Cestnik, Aug 27 2017