A175277 Base-5 pandigital primes: primes having at least one of each digit 0,1,2,3,4, when written in base 5.

3319, 3323, 3347, 3469, 3491, 3539, 3547, 3559, 3571, 3607, 3613, 3617, 3691, 3823, 3847, 3863, 4019, 4079, 4139, 4327, 4423, 4483, 4493, 4519, 4523, 4603, 4759, 4903, 4951, 5039, 5059, 5107, 5113, 5147, 5179, 5227, 5273, 5279, 5351, 5477, 5507, 5527

Offset: 1

Author

M. F. Hasler, May 27 2010

Keywords

• nonn
• base

Comments

Terms in this sequence have at least 6 digits in base 5, i.e., are larger than 5^5, since sum(d_i 5^i) = sum(d_i) (mod 4), and 0+1+2+3+4 is divisible by 2. So the smallest ones should be of the form "10...." in base 5, where "...." is a permutation of "1234". By chance the identical permutation already yields a prime, i.e. a(1) = "101234" in base 5.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Harvey P. Dale)
• Alonso Del Arte, Classifications of prime numbers - By representation in specific bases, OEIS Wiki as of Mar 19 2010.

Crossrefs

Cf. A050288, A138837, A175271, A175272, A175273, A175274, A175275, A175276, A175278, A175279, A175280.

Programs

Mathematica

Select[Prime[Range[800]],Min[DigitCount[#,5]]>0&] (* Harvey P. Dale, Mar 10 2019 *)

PARI

base(n,b=5,s=0)={local(a=[n%b]);while(09,s,48)+a[i])),a)}
forprime(p=5^5,5^6,#Set(base(p,5))==5 & print1(p","))