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A077717
Primes which can be expressed as a sum of distinct powers of 3.
11
3, 13, 31, 37, 109, 271, 283, 337, 733, 739, 757, 769, 811, 823, 1009, 1063, 1093, 2269, 2281, 2467, 2521, 2539, 2551, 2917, 2953, 3001, 3037, 3163, 3169, 3187, 3253, 3271, 6571, 6673, 6679, 6841, 7321, 7411, 7537, 7561, 7573, 8761, 8779, 8839, 9001
OFFSET
1,1
COMMENTS
Primes whose base 3 representation contains only 0's and 1's.
LINKS
EXAMPLE
31 = 3^3 + 3 + 1 belongs to this sequence.
MATHEMATICA
Select[FromDigits[#, 3]&/@Tuples[{0, 1}, 10], PrimeQ] (* Harvey P. Dale, Mar 30 2015 *)
PROG
(PARI) print1(3); forstep(n=3, 1e3, 2, if(isprime(t=fromdigits(binary(n), 3)), print1(", "t))) \\ Charles R Greathouse IV, Mar 28 2022
(PARI) is_A077717(n)=vecmax(digits(n, 3))<2 && isprime(n)
select(is_A077717, [1..9111]) \\ M. F. Hasler, Feb 15 2023
(Python)
def is_A077717(n): return A039966(n) and A010051(n) # M. F. Hasler, Feb 15 2023
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Nov 19 2002
EXTENSIONS
More terms from John W. Layman, Nov 22 2002
STATUS
approved