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

1,1

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.

Links

Thorben Böger, Table of n, a(n) for n = 1..19999

Example

a(7) = 1471 as 1471 is prime and 2000111 in base 3, which is balanced: 3*2 = 1*1 + 2*1 + 3*1.

Prog

(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)))]
(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

Crossrefs

Cf. A029971, A256083, A256076, A000040.

Sequence in context: A188127 A142813 A202083 * A136080 A215864 A190307

Adjacent sequences: A330488 A330489 A330490 * A330492 A330493 A330494

Keyword

nonn,base

Author

Thorben Böger, Dec 16 2019

Status

approved