A301797 a(n) = (4^prime(n) - 1)/3.

5, 21, 341, 5461, 1398101, 22369621, 5726623061, 91625968981, 23456248059221, 96076792050570581, 1537228672809129301, 6296488643826193618261, 1611901092819505566274901, 25790417485112089060398421, 6602346876188694799461995861, 27043212804868893898596335048021

Offset

1,1

Comments

Also, numbers with a prime number of bits 1 (cf. A001348), interleaved with bits 0. Or: odd numbers with alternating binary digits and a prime Hamming weight A000120, cf. A052294. - M. F. Hasler, Oct 16 2018

Links

Table of n, a(n) for n=1..16.

Opinions on Puzzling.StackExchange about this sequence

Formula

a(n) = A002450(A000040(n)). - Michel Marcus, Mar 27 2018

Example

For n = 1, the first prime number is 2, so a(1) = (4^2-1)/3 = (16-1)/3 = 15/3 = 5;
for n = 2, prime(2) = 3, so a(2) = (4^3-1)/3 = (64-1)/3 = 63/3 = 21;
for n = 5, prime(5) = 11, so a(5) = (4^(11)-1)/3 = (4194304-1)/3 = 4194303/3 = 1398101.

Mathematica

a[n_]:=(4^Prime[n] - 1)/3; Array[a, 50] (* Stefano Spezia, Oct 16 2018 *)

Prog

(Java) public static int a(int n){ int p = 1; while(n > 0){ p++; if(!new String(new char[p]).matches("(..+?)\\1+|.?")){ n--; } } return ((int) Math.pow(4, p)-1)/3; }
(PARI) a(n) = (4^prime(n) - 1)/3; \\ Michel Marcus, Mar 27 2018
(Magma) [(4^NthPrime(n) - 1)/3: n in [1..20]]; // Vincenzo Librandi, Oct 17 2018

Crossrefs

Cf. A000040, A000120.

Subsequence of A006995 and of A002450, which is a subsequence of A000975.

Also the intersection of A002450 and A052294.

Sequence in context: A241467 A267020 A141798 * A015461 A101694 A006109

Adjacent sequences: A301794 A301795 A301796 * A301798 A301799 A301800

Keyword

nonn,easy

Author

André Dalwigk, Mar 26 2018

Status

approved