A077717 Primes which can be expressed as a sum of distinct powers of 3.

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

Harvey P. Dale, Table of n, a(n) for n = 1..10000

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

Crossrefs

Cf. A020449, A077718, A077719, A077720, A077721, A077722, A077724.

Sequence in context: A273769 A097955 A320587 * A235265 A347988 A275081

Adjacent sequences: A077714 A077715 A077716 * A077718 A077719 A077720

Keyword

nonn,easy

Author

Amarnath Murthy, Nov 19 2002

Extensions

More terms from John W. Layman, Nov 22 2002

Status

approved