A079651 Prime numbers using only the straight digits 1, 4 and 7.

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

1,1

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Chris K. Caldwell and G. L. Honaker, Jr., 1447, Prime Curios! [Gupta]

Example

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

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} &]

Prog

(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

Crossrefs

Cf. A028373.

Sequence in context: A158594 A215419 A107642 * A178386 A097956 A094104

Adjacent sequences: A079648 A079649 A079650 * A079652 A079653 A079654

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jan 23 2003

Extensions

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

Status

approved