A226227 Numbers m such that all lengths of runs of 0's in the binary representation of m are prime numbers.

1, 3, 4, 7, 8, 9, 12, 15, 17, 19, 24, 25, 28, 31, 32, 35, 36, 39, 49, 51, 56, 57, 60, 63, 65, 68, 71, 72, 73, 76, 79, 96, 99, 100, 103, 113, 115, 120, 121, 124, 127, 128, 131, 136, 137, 140, 143, 145, 147, 152, 153, 156, 159, 193, 196, 199, 200, 201, 204, 207, 224, 227

Offset: 1

Author

Alex Ratushnyak, May 31 2013

Keywords

• nonn
• base

Comments

Numbers with no 0's in base 2 (that is, 2^k - 1) are included.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033015, A226228, A226229.

Cf. A005811, A030308, A010051.

Programs

C

#include 
#include 
typedef unsigned long long U64;
U64 runs[] = {0,2,3,5,7,11,13,17,19,23,29,31,37,41,43}, *wr;
#define MemUSAGE 1ULL<<33
#define TOP (1ULL<<9)  // <<40 ok if MemUSAGE = 1ULL<<33
int compare64(const void *p1, const void *p2) {
  if (*(U64*)p1 == *(U64*)p2) return 0;
  return (*(U64*)p1 < *(U64*)p2) ? -1 : 1;
}
void rec(U64 bits) {
  for (U64 i = 0, b; (b = bits << runs[i]) < TOP; ++i)
    *wr++ = b, rec(b*2+1);
}
int main() {
  U64 *wr0 = (wr = (U64*)malloc(MemUSAGE));
  rec(1);
  //printf("%llu\n", wr-wr0);
  qsort(wr0, wr-wr0, 8, compare64);
  while (wr0
				

Haskell

import Data.List (group, genericLength)
a226227 n = a226227_list !! (n-1)
a226227_list = filter (all (== 1) .
               map (a010051 . genericLength) .
                   other . tail . reverse . group . a030308_row) [1..]
   where other [] = []; other [x] = [x]; other (x:_:xs) = x : other xs
-- Reinhard Zumkeller, Jun 05 2013

Mathematica

Select[Range@227, And @@ PrimeQ[(Length /@ Split@ IntegerDigits[#, 2])[[2 ;; ;; 2]]] &] (* Giovanni Resta, Jun 01 2013 *)
Select[Range[250],AllTrue[Length/@Select[Split[IntegerDigits[#,2]],MemberQ[ #,0]&],PrimeQ]&] (* Harvey P. Dale, Aug 07 2021 *)