A360502 - OEIS

%I #40 Apr 19 2023 11:31:44

%S 1,12,1210,121011,12101112,1210111220,121011122021,12101112202122,

%T 12101112202122100,12101112202122100101,12101112202122100101102,

%U 12101112202122100101102110,12101112202122100101102110111,12101112202122100101102110111112,12101112202122100101102110111112120

%N Concatenate the ternary strings for 1,2,...,n.

%C 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.

%C 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.

%C When read as decimal numbers, the first prime is a(7315), with 56003 digits. - _Michael S. Branicky_, Apr 18 2023

%H Winston de Greef, <a href="/A360502/b360502.txt">Table of n, a(n) for n = 1..222</a>

%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>

%e a(4): concatenate 1, 2, 10, 11, getting 121011.

%p a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(

%p       a(n-1), seq(l[-i], i=1..nops(l)))))(convert(n, base, 3)))

%p     end:

%p seq(a(n), n=1..15);  # _Alois P. Heinz_, Feb 17 2023

%t nn = 15; s = IntegerDigits[Range[nn], 3]; Array[FromDigits[Join @@ s[[1 ;; #]]] &, nn] (* _Michael De Vlieger_, Apr 19 2023 *)

%o (Python)

%o from sympy.ntheory import digits

%o def a(n): return int("".join("".join(map(str, digits(k, 3)[1:])) for k in range(1, n+1)))

%o print([a(n) for n in range(1, 16)]) # _Michael S. Branicky_, Feb 18 2023

%o (Python) # faster version for initial segment of sequence

%o from sympy.ntheory import digits

%o from itertools import count, islice

%o def agen(s=""): yield from (int(s:=s+"".join(map(str, digits(n, 3)[1:]))) for n in count(1))

%o print(list(islice(agen(), 15))) # _Michael S. Branicky_, Feb 18 2023

%Y Cf. A007089, A036954, A360503, A360504.

%Y This is the ternary analog of A007908.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Feb 16 2023