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

Author

Thorben Böger, Dec 16 2019

Keywords

• nonn
• base

Comments

A number is called "balanced" here if the sum of digits weighted by their arithmetic distance from the "center" of the number is zero. Palindromic primes (A029971) are "trivially" balanced, so they are excluded here.

These are the primes in A256083, respectively the intersection of A000040 and A256083.

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

Crossrefs

Cf. A029971, A256083, A256076, A000040.

Programs

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)))]