A372770 Primes in A284798.

13, 97, 853, 1021, 1093, 7873, 8161, 8377, 9337, 12241, 62989, 63853, 66733, 74797, 79861, 81373, 82021, 84181, 86413, 91381, 92317, 94477, 95773, 98893, 100189, 101701, 111997, 114157, 534841, 552553, 556441, 560977, 578689, 580633, 591937, 600361, 631249

Offset

1,1

Comments

The base-b expansion (d_1)(d_2)...(d_m) of a number is antipalindromic if, for each of its m digits, it holds that d_k + d_{m-k+1} = b-1.

In a base other than 3, there is at most a single antipalindromic prime.

Links

Table of n, a(n) for n=1..37.

Lubomira Dvorakova, Stanislav Kruml, and David Ryzák, Antipalindromic numbers, arXiv:2008.06864 [math.CO], 2020.

Example

For m = 3, the only solution is 13 = 111_3.
For m = 5, the only solution is 97 = 10121_3.

Mathematica

Select[Prime[Range[52000]], FromDigits[Reverse[2 - IntegerDigits[#, 3]], 3] == # &] (* Amiram Eldar, Jun 16 2024 *)

Prog

(Python)
from sympy import isprime
from itertools import count, islice, product
def bgen(): # generator of terms of A284798
    yield 1
    for d in count(2):
        for first in [1, 2]:
            for rest in product([0, 1, 2], repeat=(d-2)//2):
                left, mid = (first, ) + rest, (1, ) if d&1 else tuple()
                right = tuple([2-d for d in left][::-1])
                yield int("".join(str(d) for d in left + mid + right), 3)
def agen(): yield from filter(isprime, bgen())
print(list(islice(agen(), 40))) # Michael S. Branicky, Jun 16 2024

Crossrefs

Cf. A284798.

Sequence in context: A198480 A126508 A228680 * A158795 A075899 A006976

Adjacent sequences: A372767 A372768 A372769 * A372771 A372772 A372773

Keyword

base,nonn,easy,new

Author

Stanislav Kruml, May 12 2024

Status

approved