OFFSET
1,2
COMMENTS
If the terms are read as ternary strings and converted to base 10, we get A260853. For example, a(3) = 121021_3 = 439_10, which is A260853(3). This is a prime. What is the next prime term?
If the terms are read as decimal numbers, which of them are primes? a(3) = 121021_10 is a decimal prime, but what is the next one? It is a surprise that 121021 is a prime in both base 3 and base 10.
LINKS
EXAMPLE
To get a(3) we concatenate 1, 2, 10, 2, and 1, getting 121021.
MAPLE
t:= n-> (l-> parse(cat(seq(l[-i], i=1..nops(l)))))(convert(n, base, 3)):
a:= n-> parse(cat(map(t, [$1..n, n-i$i=1..n-1])[])):
seq(a(n), n=1..12); # Alois P. Heinz, Feb 17 2023
MATHEMATICA
Table[FromDigits[Flatten[Join[IntegerDigits[#, 3]&/@Range[n], IntegerDigits[#, 3]&/@ Range[ n-1, 1, -1]]]], {n, 20}] (* Harvey P. Dale, Oct 01 2023 *)
PROG
(Python)
from sympy.ntheory import digits
def a(n): return int("".join("".join(map(str, digits(k, 3)[1:])) for k in list(range(1, n+1))+list(range(n-1, 0, -1))))
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Feb 18 2023
(Python) # faster version for initial segment of sequence
from sympy.ntheory import digits
from itertools import count, islice
def agen(): # generator of terms
sf, sr = "", ""
for n in count(1):
sn = "".join(map(str, digits(n, 3)[1:]))
sf += sn
yield int(sf + sr)
sr = sn + sr
print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 18 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Feb 17 2023
STATUS
approved