A226228 Numbers m such that all lengths of runs of 1's in the binary representation of m are prime numbers.

3, 6, 7, 12, 14, 24, 27, 28, 31, 48, 51, 54, 55, 56, 59, 62, 96, 99, 102, 103, 108, 110, 112, 115, 118, 119, 124, 127, 192, 195, 198, 199, 204, 206, 216, 219, 220, 223, 224, 227, 230, 231, 236, 238, 248, 251, 254, 384, 387, 390, 391, 396, 398, 408, 411, 412, 415, 432

Offset

1,1

Links

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

Mathematica

Select[Range@432, And @@ PrimeQ[(Length /@ Split@ IntegerDigits[#, 2])[[;; ;; 2]]] &] (* Giovanni Resta, Jun 01 2013 *)

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*2+1) << runs[i])-1) < TOP; ++i)
    if (b) *wr++ = b, rec(b);
}
int main() {
  U64 *wr0 = (wr = (U64*)malloc(MemUSAGE));
  rec(0);
  //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)
a226228 n = a226228_list !! (n-1)
a226228_list = filter (all (== 1) .
               map (a010051 . genericLength) .
                   other . reverse . group . a030308_row) [1..]
   where other [] = []; other [x] = [x]; other (x:_:xs) = x : other xs
-- Reinhard Zumkeller, Jun 05 2013

Crossrefs

Cf. A033015, A226227, A226229.

Cf. A005811, A030308, A010051.

Sequence in context: A175332 A022434 A242666 * A365422 A335431 A269174

Adjacent sequences: A226225 A226226 A226227 * A226229 A226230 A226231

Keyword

nonn,base

Author

Alex Ratushnyak, May 31 2013

Status

approved