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

1,2

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

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 *)

Prog

(C)
#include <stdio.h>
#include <stdlib.h>
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<wr)  printf("%llu, ", *wr0++);
  return 0;
}
(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

Crossrefs

Cf. A033015, A226228, A226229.

Cf. A005811, A030308, A010051.

Sequence in context: A183988 A175054 A154366 * A319736 A100452 A004201

Adjacent sequences: A226224 A226225 A226226 * A226228 A226229 A226230

Keyword

nonn,base

Author

Alex Ratushnyak, May 31 2013

Status

approved