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, 15925587525460787671288, 429990863187441267124796

Offset: 1

Author

Patrick De Geest, May 15 1999

Keywords

• nonn
• base
• easy

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

Examples

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

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

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.

Programs

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

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 *)