A330491 Non-palindromic balanced primes in base 3.
137, 991, 1109, 1237, 1291, 1301, 1471, 1663, 1721, 1861, 1871, 7057, 7219, 7507, 7537, 7699, 8291, 8597, 8707, 9091, 9587, 9697, 9857, 10159, 10163, 10211, 10273, 10321, 10627, 10631, 10739, 11027, 11437, 11551, 11777, 11887, 12239, 12401, 12659, 12671, 12821
Offset: 1
Examples
a(7) = 1471 as 1471 is prime and 2000111 in base 3, which is balanced: 3*2 = 1*1 + 2*1 + 3*1.
Links
- Thorben Böger, Table of n, a(n) for n = 1..19999
Programs
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PARI
ok(n)={my(v=digits(n,3)); isprime(n) && !sum(i=1, #v, v[i]*((#v+1)/2-i)) && Vecrev(v)<>v} \\ Andrew Howroyd, Dec 23 2019 -
Python
from primes_file import primes#list containing first 3 million primesfrom baseconvert import base as bdef isbalanced(converted): return sum([(place - (len(converted)/2 - 0.5))*digit for place, digit in enumerate(converted)]) == 0balanced_primes_list = [prime for prime in primes if(b(prime, 10, 3) != b(prime, 10, 3)[::-1] and isbalanced(b(prime, 10, 3)))]
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