A360504 Concatenate the ternary strings for 1,2,...,n-1, n, n-1, ..., 2,1.

1, 121, 121021, 1210111021, 12101112111021, 121011122012111021, 1210111220212012111021, 12101112202122212012111021, 1210111220212210022212012111021, 1210111220212210010110022212012111021, 1210111220212210010110210110022212012111021, 1210111220212210010110211010210110022212012111021

Offset: 1

Author

N. J. A. Sloane, Feb 17 2023

Keywords

• nonn
• base

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.

Examples

			To get a(3) we concatenate 1, 2, 10, 2, and 1, getting 121021.
		

Links

• Winston de Greef, Table of n, a(n) for n = 1..123
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A007089, A360502, A360503.

This is the ternary analog of A173426.

Programs

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 *)

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