A192448 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.

367, 389, 27059, 27241, 33577, 49499, 50789, 77023, 103643, 108211, 119591, 122117, 131111, 131113, 133733, 139309, 139339, 141601, 141629, 146221, 167213, 169489, 171161, 182443, 192383, 204913, 205957, 211559, 213901, 215183, 229591, 233161, 257783, 260387

Offset

1,1

Comments

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.

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

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

The progression of L from 2 to 359 (primes 17-353 replaced by dots for brevity):
  2: 0010000000
  3: 0011000000
  5: 0011010000
  7: 0011010100
11: 0011010100
13: 0110010100
...
359: 1110110011
The next prime, 367, toggles the 4th, 7th, and 8th digits of L giving 1111111111, so 367 is a member of the sequence.
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.
The next member of the sequence, 389, occurs three primes later:
379: 1110111110
383: 1110111100
389: 1111111111

Maple

A192448 := proc(nmax) local Lf, p, l, d, wrks ;
        Lf := vector([seq(0, i=0..9)]) ;
        p := 2;
        for l from 1 to nmax do
                for d in convert(p, base, 10) do
                        Lf[d+1] := Lf[d+1]+1 ;
                end do:
                wrks := true;
                for i from 1 to 10 do
                        if type(Lf[i], 'even') then
                                wrks := false;
                                break;
                        end if;
                end do:
                if wrks then
                        print(p);
                end if;
                p := nextprime(p) ;
        end do:
        return ;
end proc:
A192448(20000) ; # R. J. Mathar, Jul 12 2011

Crossrefs

Sequence in context: A286793 A079493 A080020 * A118566 A320711 A142236

Adjacent sequences: A192445 A192446 A192447 * A192449 A192450 A192451

Keyword

nonn,base

Author

Gil Broussard, Jul 02 2011

Status

approved