A175277 - OEIS

%I #13 Apr 13 2021 07:15:35

%S 3319,3323,3347,3469,3491,3539,3547,3559,3571,3607,3613,3617,3691,

%T 3823,3847,3863,4019,4079,4139,4327,4423,4483,4493,4519,4523,4603,

%U 4759,4903,4951,5039,5059,5107,5113,5147,5179,5227,5273,5279,5351,5477,5507,5527

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

%C 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.

%H Amiram Eldar, <a href="/A175277/b175277.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2500 from Harvey P. Dale)

%H Alonso Del Arte, <a href="http://oeis.org/wiki/Classifications_of_prime_numbers#By_representation_in_specific_bases">Classifications of prime numbers - By representation in specific bases</a>, OEIS Wiki as of Mar 19 2010.

%t Select[Prime[Range[800]],Min[DigitCount[#,5]]>0&] (* _Harvey P. Dale_, Mar 10 2019 *)

%o (PARI) base(n,b=5,s=0)={local(a=[n%b]);while(0<n\=b,a=concat(n%b,a));if(s,s=32*s+23;Strchr(vectorsmall(#a,i,if(a[i]>9,s,48)+a[i])),a)}

%o forprime(p=5^5,5^6,#Set(base(p,5))==5 & print1(p","))

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, May 27 2010