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
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, May 31 2013
STATUS
approved