A048435 Take the first n numbers written in base 3, concatenate them, then convert from base 3 to base 10.

1, 5, 48, 436, 3929, 35367, 318310, 2864798, 77349555, 2088437995, 56387825876, 1522471298664, 41106725063941, 1109881576726421, 29966802571613382, 809103669433561330, 21845799074706155927, 589836575017066210047

Offset

1,2

Comments

The first three primes in this sequence occur for n = 2 (a(2) = 5), n = 5 (a(5) = 3929), and n = 82 (a(82) = 1.1247...*10^140). - Kurt Foster, Oct 24 2015 [Comment added by N. J. A. Sloane, Oct 25 2015]

According to a comment made by Jeff Peltier following the "Most Wanted Prime" video, n = 2546 also gives a prime. See A360503. - N. J. A. Sloane, Feb 17 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Brady Haran and N. J. A. Sloane, Most Wanted Prime, Numberphile video, December 2021.

Index entries for sequences related to Most Wanted Primes video

Example

a(6): (1)(2)(10)(11)(12)(20) = 1210111220_3 = 35367.

Mathematica

If[STARTPOINT==1, n={}, n=Flatten[IntegerDigits[Range[STARTPOINT-1], 3]]]; Table[AppendTo[n, IntegerDigits[w, 3]]; n=Flatten[n]; FromDigits[n, 3], {w, STARTPOINT, ENDPOINT}] (* Dylan Hamilton, Aug 09-04 2010 *)
f[n_]:= FromDigits[Flatten@IntegerDigits[Range@n, 3], 3]; Array[f, 20] (* Vincenzo Librandi, Dec 30 2012 *)

Prog

(Magma) [n eq 1 select 1 else Self(n-1)*3^(1+Ilog(3, n))+n: n in [1..20]]; // Vincenzo Librandi, Dec 30 2012

Crossrefs

Primes: A360503.

Concatenation of first n numbers in other bases: 2: A047778, 3: this sequence, 4: A048436, 5: A048437, 6: A048438, 7: A048439, 8: A048440, 9: A048441, 10: A007908, 11: A048442, 12: A048443, 13: A048444, 14: A048445, 15: A048446, 16: A048447.

Sequence in context: A268736 A247769 A116431 * A293102 A023999 A126224

Adjacent sequences: A048432 A048433 A048434 * A048436 A048437 A048438

Keyword

nonn,base,easy

Author

Patrick De Geest, May 15 1999

Status

approved