A079651 Primes having only {1, 4, 7} as digits.

7, 11, 17, 41, 47, 71, 1117, 1171, 1447, 1471, 1741, 1747, 1777, 4111, 4177, 4441, 4447, 7177, 7411, 7417, 7477, 7717, 7741, 11117, 11171, 11177, 11411, 11447, 11471, 11717, 11777, 14177, 14411, 14447, 14717, 14741, 14747, 14771, 17117, 17417

Offset: 1

Author

Shyam Sunder Gupta, Jan 23 2003

Keywords

• base
• nonn

Comments

The number of decimal digits of a(n) is never divisible by 3. - Robert Israel, May 22 2014

The smallest prime using only all three straight digits is a(9) = 1447 (see Prime Curios! link). - Bernard Schott, Sep 08 2023

Examples

			17 is a term because it is a prime and consists of straight digits 1 and 7 only.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Chris K. Caldwell and G. L. Honaker, Jr., 1447, Prime Curios! [Gupta]
• Index to entries for primes with digits in a given set

Crossrefs

Cf. A028373.

Programs

Maple

f:= proc(x) local n,d,t,i,a;
n:= floor(log[3]((2*x+3)));
if n mod 3 = 0 then return 0 fi;
d:=x - (3^n - 3)/2;
t:= 0;
for i from 0 to n-1 do
   a:= d mod 3;
   t:= t + (3*a+1)*10^i;
   d:= (d-a)/3;
od:
t
end proc:
select(isprime, map(f, [$1..1000])); # Robert Israel, May 22 2014

Mathematica

Select[Prime[Range[2000]], Union[ Join[ IntegerDigits[ # ], {1, 4, 7}]] == {1, 4, 7} &]

PARI

straight(n)=my(t);while(n,t=n%10;if(t!=1&&t!=4&&t!=7,return(0));n\=10);!!t
select(straight, primes(1000)) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

Corrected and extended by Robert G. Wilson v, Jan 24 2003