A092619 Numbers with property that number of prime digits is prime.
22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 122, 123, 125, 127, 132, 133, 135, 137, 152, 153, 155, 157, 172, 173, 175, 177, 202, 203, 205, 207, 212, 213, 215, 217, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234
Offset: 1
Examples
22 has two prime digits and their number 2 is prime, so 22 is a term. 222 has three prime digits and their number 3 is prime, so 222 is a term.
Crossrefs
Cf. A085557.
Programs
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Maple
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); # second Maple program: q:= n-> isprime(nops(select(isprime, convert(n, base, 10)))): select(q, [$1..500])[]; # Alois P. Heinz, Feb 08 2023
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Mathematica
Select[Range[250],PrimeQ[Count[IntegerDigits[#],?PrimeQ]]&] (* _Harvey P. Dale, Nov 29 2011 *)
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Python
from itertools import count, islice from sympy import isprime def A092619_gen(startvalue=1): # generator of terms >= startvalue return filter(lambda n:isprime(sum(1 for d in str(n) if d in {'2','3','5','7'})),count(max(startvalue,1))) A092619_list = list(islice(A092619_gen(),20)) # Chai Wah Wu, Feb 08 2023
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