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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A078348 A078963 A236643 * A209206 A252510 A253872

Adjacent sequences: A175274 A175275 A175276 * A175278 A175279 A175280

Keyword

nonn,base

Author

M. F. Hasler, May 27 2010

Status

approved