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A360502
Concatenate the ternary strings for 1,2,...,n.
10
1, 12, 1210, 121011, 12101112, 1210111220, 121011122021, 12101112202122, 12101112202122100, 12101112202122100101, 12101112202122100101102, 12101112202122100101102110, 12101112202122100101102110111, 12101112202122100101102110111112, 12101112202122100101102110111112120
OFFSET
1,2
COMMENTS
If the terms are read as ternary strings and converted to base 10, we get A048435. For example, a(2) = 12_3 = 5_10, which is A048435(2). This is a prime, and gives the first term of A360503.
If the terms are read as decimal numbers, which of them are primes? 12101112202122100101102110111, for example, is not a prime, since it is 37*327057086543840543273030003.
When read as decimal numbers, the first prime is a(7315), with 56003 digits. - Michael S. Branicky, Apr 18 2023
EXAMPLE
a(4): concatenate 1, 2, 10, 11, getting 121011.
MAPLE
a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
a(n-1), seq(l[-i], i=1..nops(l)))))(convert(n, base, 3)))
end:
seq(a(n), n=1..15); # Alois P. Heinz, Feb 17 2023
MATHEMATICA
nn = 15; s = IntegerDigits[Range[nn], 3]; Array[FromDigits[Join @@ s[[1 ;; #]]] &, nn] (* Michael De Vlieger, Apr 19 2023 *)
PROG
(Python)
from sympy.ntheory import digits
def a(n): return int("".join("".join(map(str, digits(k, 3)[1:])) for k in range(1, n+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(s=""): yield from (int(s:=s+"".join(map(str, digits(n, 3)[1:]))) for n in count(1))
print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 18 2023
CROSSREFS
This is the ternary analog of A007908.
Sequence in context: A229691 A180586 A178529 * A201642 A177090 A103269
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Feb 16 2023
STATUS
approved