cp's OEIS Frontend

A092619 Numbers with property that number of prime digits is prime.

%I A092619 #20 Jun 26 2025 14:47:48
%S A092619 22,23,25,27,32,33,35,37,52,53,55,57,72,73,75,77,122,123,125,127,132,
%T A092619 133,135,137,152,153,155,157,172,173,175,177,202,203,205,207,212,213,
%U A092619 215,217,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234
%N A092619 Numbers with property that number of prime digits is prime.
%C A092619 A subset of A085557 from the 4th term.
%C A092619 Upper relative density in the primes is 1; lower relative density in the primes is 0. - _Charles R Greathouse IV_, Nov 14 2010
%e A092619 22 has two prime digits and their number 2 is prime, so 22 is a term.
%e A092619 222 has three prime digits and their number 3 is prime, so 222 is a term.
%p A092619 stev_sez:=proc(n) local i, tren, st, ans,anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr:=proc(n) local i, stpf, ans, ans1; ans:=[ ]: stpf:=0: for i from 1 to n do if (isprime( ts_stpf(i) )='true') then ans:=[ op(ans), i ]: fi od; RETURN(ans) end: ts_pr(300);
%p A092619 # second Maple program:
%p A092619 q:= n-> isprime(nops(select(isprime, convert(n, base, 10)))):
%p A092619 select(q, [$1..500])[];  # _Alois P. Heinz_, Feb 08 2023
%t A092619 Select[Range[250],PrimeQ[Count[IntegerDigits[#],_?PrimeQ]]&] (* _Harvey P. Dale_, Nov 29 2011 *)
%o A092619 (Python)
%o A092619 from itertools import count, islice
%o A092619 from sympy import isprime
%o A092619 def A092619_gen(startvalue=1): # generator of terms >= startvalue
%o A092619     return filter(lambda n:isprime(sum(1 for d in str(n) if d in {'2','3','5','7'})),count(max(startvalue,1)))
%o A092619 A092619_list = list(islice(A092619_gen(),20)) # _Chai Wah Wu_, Feb 08 2023
%Y A092619 Cf. A085557.
%K A092619 nonn,base
%O A092619 1,1
%A A092619 _Jani Melik_, Apr 11 2004