cp's OEIS Frontend

A082555 Primes whose base-3 representation does not contain a 0.

%I A082555 #21 Jun 03 2025 01:12:03
%S A082555 2,5,7,13,17,23,41,43,53,67,71,79,131,149,151,157,211,229,233,239,241,
%T A082555 367,373,401,449,457,607,617,619,643,647,691,701,719,727,1093,1097,
%U A082555 1103,1123,1129,1187,1201,1213,1367,1373,1427,1429,1447,1453,1823,1831,1861
%N A082555 Primes whose base-3 representation does not contain a 0.
%C A082555 Primes in A032924. - _Robert Israel_, Dec 28 2018
%C A082555 The analog "primes without digit 2 in ternary" is A077717. There is no prime > 2 not having the digit 1 in ternary, since then the number is divisible by 2. - _M. F. Hasler_, Feb 15 2023
%H A082555 Robert Israel, <a href="/A082555/b082555.txt">Table of n, a(n) for n = 1..10000</a>
%e A082555 41 = 1112_3, which contains no 0.
%p A082555 select(t -> isprime(t) and not(has(convert(t,base,3),0)), [2,seq(i,i=5..10000,2)]); # _Robert Israel_, Dec 28 2018
%o A082555 (PARI) dec3(s)=while(s>0,if(s%3==0,return(0),s=floor(s/3))); return(1)
%o A082555 forprime(i=1,20000,if(dec3(i)==1,print1(i,", "),))
%o A082555 (Python)
%o A082555 def is_A082555(n): return is_A032924(n) and A010051(n)
%o A082555 [p for p in range(1888) if is_A082555(p)] # _M. F. Hasler_, Feb 15 2023
%Y A082555 Cf. A032924 (numbers without digit 0 in base 3), A073779, A077267.
%Y A082555 Cf. A077717 (primes that are the sum of distinct powers of 3 <=> base-3 representation does not contain a digit 2).
%K A082555 base,nonn
%O A082555 1,1
%A A082555 _Randy L. Ekl_, May 03 2003