A192448 - OEIS

%I #26 Feb 27 2019 01:18:34

%S 367,389,27059,27241,33577,49499,50789,77023,103643,108211,119591,

%T 122117,131111,131113,133733,139309,139339,141601,141629,146221,

%U 167213,169489,171161,182443,192383,204913,205957,211559,213901,215183,229591,233161,257783,260387

%N Primes that indicate that the total frequency of every decimal digit in the set of all primes up to and including that prime is odd.

%C Initialize a binary register L for the ten digits to zero (0000000000); cumulatively toggle the N-th digit of L for every digit N as we wander through the primes.  Primes P such that L is 1111111111 after including the digits of P are added to the sequence.

%C L is 1111111111 when all of the digits in the current and preceding primes have simultaneously occurred an odd number of times.

%H Donovan Johnson, <a href="/A192448/b192448.txt">Table of n, a(n) for n = 1..1000</a>

%e The progression of L from 2 to 359 (primes 17-353 replaced by dots for brevity):

%e   2: 0010000000

%e   3: 0011000000

%e   5: 0011010000

%e   7: 0011010100

%e 11: 0011010100

%e 13: 0110010100

%e ...

%e 359: 1110110011

%e The next prime, 367, toggles the 4th, 7th, and 8th digits of L giving 1111111111, so 367 is a member of the sequence.

%e The next prime, 373, toggles the 4th digit of L twice (no change) and toggles the 8th digit of L giving 1111111011, so 373 is excluded.

%e The next member of the sequence, 389, occurs three primes later:

%e 379: 1110111110

%e 383: 1110111100

%e 389: 1111111111

%p A192448 := proc(nmax) local Lf,p,l,d,wrks ;

%p         Lf := vector([seq(0,i=0..9)]) ;

%p         p := 2;

%p         for l from 1 to nmax do

%p                 for d in convert(p,base,10) do

%p                         Lf[d+1] := Lf[d+1]+1 ;

%p                 end do:

%p                 wrks := true;

%p                 for i from 1 to 10 do

%p                         if type(Lf[i],'even') then

%p                                 wrks := false;

%p                                 break;

%p                         end if;

%p                 end do:

%p                 if wrks then

%p                         print(p);

%p                 end if;

%p                 p := nextprime(p) ;

%p         end do:

%p         return ;

%p end proc:

%p A192448(20000) ; # _R. J. Mathar_, Jul 12 2011

%K nonn,base

%O 1,1

%A _Gil Broussard_, Jul 02 2011