A360502 Concatenate the ternary strings for 1,2,...,n.

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

Links

Winston de Greef, Table of n, a(n) for n = 1..222

Index entries for sequences related to Most Wanted Primes video

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

Cf. A007089, A036954, A360503, A360504.

This is the ternary analog of A007908.

Sequence in context: A229691 A180586 A178529 * A201642 A177090 A103269

Adjacent sequences: A360499 A360500 A360501 * A360503 A360504 A360505

Keyword

nonn,base

Author

N. J. A. Sloane, Feb 16 2023

Status

approved