A084986 Duplicate of A034844.
11, 19, 41, 61, 89, 101, 109, 149, 181, 191, 199, 401, 409, 419, 449, 461, 491, 499, 601
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a019546 n = a019546_list !! (n-1)
a019546_list = filter (all (`elem` "2357") . show )
([2,3,5] ++ (drop 2 a003631_list))
-- Or, much more efficient:
a019546_list = filter ((== 1) . a010051) $
[2,3,5,7] ++ h ["3","7"] where
h xs = (map read xs') ++ h xs' where
xs' = concat $ map (f xs) "2357"
f xs d = map (d :) xs
-- Reinhard Zumkeller, Jul 19 2011
[p: p in PrimesUpTo(5600) | Set(Intseq(p)) subset [2,3,5,7]]; // Bruno Berselli, Jan 13 2012
Select[Prime[Range[700]], Complement[IntegerDigits[#], {2, 3, 5, 7}] == {} &] (* Alonso del Arte, Aug 27 2012 *)
Select[Prime[Range[700]], AllTrue[IntegerDigits[#], PrimeQ] &] (* Ivan N. Ianakiev, Jun 23 2018 *)
Select[Flatten[Table[FromDigits/@Tuples[{2,3,5,7},n],{n,4}]],PrimeQ] (* Harvey P. Dale, Apr 05 2025 *)
is_A019546(n)=isprime(n) & !setminus(Set(Vec(Str(n))),Vec("2357")) \\ M. F. Hasler, Jan 13 2012
print1(2); for(d=1,4, forstep(i=1,4^d-1,[1,1,2], p=sum(j=0,d-1,10^j*[2,3,5,7][(i>>(2*j))%4+1]); if(isprime(p), print1(", "p)))) \\ Charles R Greathouse IV, Apr 29 2015
from itertools import product from sympy import isprime A019546_list = [2,3,5,7]+[p for p in (int(''.join(d)+e) for l in range(1,5) for d in product('2357',repeat=l) for e in '37') if isprime(p)] # Chai Wah Wu, Jun 04 2021
166 has digits 1 and 6 and they are nonprime digits. a(1000) = 8686. a(10^4) = 118186 a(10^5) = 4090986. a(10^6) = 66466686.
a084984 n = a084984_list !! (n-1) a084984_list = filter (not . any (`elem` "2357") . show ) [0..] -- Reinhard Zumkeller, Jul 19 2011
[n: n in [0..169] | forall{d: d in [2,3,5,7] | d notin Set(Intseq(n))}]; // Bruno Berselli, Jul 19 2011
npdQ[n_]:=And@@Table[FreeQ[IntegerDigits[n],i],{i,{2,3,5,7}}]; Select[ Range[ 0,200],npdQ] (* Harvey P. Dale, Jul 22 2013 *)
is(n)=isprime(eval(Vec(Str(n))))==0 \\ Charles R Greathouse IV, Feb 20 2012
my(table=[0,1,4,6,8,9]); \ a(n) = fromdigits([table[d+1] |d<-digits(n-1,6)]); \\ Kevin Ryde, May 27 2025
149 is a term as 1, 4, 9, 14, 49 are all nonprimes. 199 is not a term as 19 is a prime.
import Data.List (elemIndices) a033274 n = a033274_list !! (n-1) a033274_list = map (a000040 . (+ 1)) $ elemIndices 0 a079066_list -- Reinhard Zumkeller, Jul 19 2011
f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 1100, f@# == 1 &] (* Robert G. Wilson v, Aug 01 2010 *)
Select[Prime[Range[1100]],NoneTrue[Flatten[Table[FromDigits/@Partition[IntegerDigits[#],d,1],{d,IntegerLength[#]-1}]],PrimeQ]&] (* Harvey P. Dale, Apr 19 2025 *)
from sympy import isprime
def ok(n):
if n in {2, 3, 5, 7}: return True
s = str(n)
if set(s) & {"2", "3", "5", "7"} or not isprime(n): return False
ss2 = set(s[i:i+l] for i in range(len(s)-1) for l in range(2, len(s)))
return not any(isprime(int(ss)) for ss in ss2)
print([k for k in range(9000) if ok(k)]) # Michael S. Branicky, Jun 29 2022
13 is prime and it has one prime digit, 3; 103 is prime and it has one prime digit, 3.
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_prn:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( isprime(i)='true' and ts_stpf(i) = 1) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_prn(1000);
podQ[n_]:=(1==Length@Select[IntegerDigits[n],PrimeQ]);Select[Prime[Range[250]],podQ](* Zak Seidov *)
isok(n) = isprime(n) && (d = digits(n)) && (sum(i=1, #d, isprime(d[i])) == 1); \\ Michel Marcus, Mar 10 2014
A092621 = list(p for p in primes(1000) if len([d for d in p.digits() if is_prime(d)]) == 1)
import Data.List (elemIndices) a179909 n = a179909_list !! (n-1) a179909_list = map (a000040 . (+ 1)) $ elemIndices 1 a079066_list -- Reinhard Zumkeller, Jul 19 2011
f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 230, f@# == 2 &]
import Data.List (elemIndices) a179919 n = a179919_list !! (n-1) a179919_list = map (a000040 . (+ 1)) $ elemIndices 11 a079066_list -- Reinhard Zumkeller, Jul 19 2011
f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 19110, f@# == 12 &]
a[n_]:=Count[PrimeQ/@IntegerDigits[Prime[n]], True]
a(n) = vecsum(apply(x->isprime(x), digits(prime(n)))); \\ Michel Marcus, Mar 15 2019
a179336 n = a179336_list !! (n-1) a179336_list = filter (any (`elem` "2357") . show ) a000040_list -- Reinhard Zumkeller, Jul 19 2011
[p: p in PrimesUpTo(5000) | Set(Intseq(p)) subset [1,4,6,8,9]]; // Vincenzo Librandi, Oct 25 2016
F:= proc(d) local T, R, L, r;
R:= NULL;
T:= combinat:-cartprod([[1,4,6,8,9]$d]);
while not T[finished] do
L:= T[nextvalue]();
r:= add(L[i]*10^(d-i),i=1..d);
if isprime(r) then R:= R,r fi
od;
R
end proc:
seq(F(d),d=2..5); # Robert Israel, Dec 07 2017
Select[Prime[Range[800]], Complement[IntegerDigits[#], {1, 4, 6, 8, 9}] == {} &] (* Vincenzo Librandi, Oct 25 2016 *)
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